<p>Considerando que os segmentos com “marcas iguais” são congruentes, determine os valores das incógnitas nos casos:</p>
<ol type=“a”>
<li>Trapézio</li>
<p style=“text-align:center;”><img 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<li>Trapézio </li>
<p style=“text-align:center;”><img src=“data:image/jpeg;base64,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”></p>
<li>Trapézio </li>
<p style=“text-align:center;”><img 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<p style=“text-align:center;”></p>
<li>Trapézio (<svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“19.58ex” height=“2.843ex” style=“vertical-align: -0.838ex;” viewBox=“0 -863.1 8430.4 1223.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title” data-mathml="undefined">
<title> M N = x - 2 y + 5 )  </title>
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Passo 1

<p>Olá, tudo bem?! Vou te ajudar a resolver essa atividade, tudo bem?</p>
<p>Aqui é o seguinte, precisamos determinar os valores das incógnitas, é isso.</p>
<p>O problema informa que <b>segmentos com marcas iguais são congruentes</b>, ou seja:</p>
<ul>
<li>Segmentos com <b>uma marca</b> têm o mesmo comprimento entre si;</li>
<li>Segmentos com <b>duas marcas</b> também são iguais entre si, mas <b>diferentes</b> dos de uma marca.</li>
</ul>
<p>Todos os casos envolvem <b>trapézios</b>, com segmentos <b>paralelos às bases</b>, o que ativa uma propriedade fundamental:</p>
<p><b>Em um trapézio, segmentos paralelos às bases e igualmente espaçados nos lados não paralelos formam uma progressão aritmética.</b></p>
<p>Essa será a ideia-chave para quase todos os itens.</p>
<p>Se vários segmentos paralelos às bases cortam os lados do trapézio em <b>partes congruentes</b>, então os comprimentos desses segmentos:</p>
<ul>
<li>Crescem ou decrescem de forma <b>linear</b>;</li>
<li>Formam uma <b>progressão aritmética (P.A.)</b>.</li>
</ul>
<p>Ou seja, a <b>diferença entre termos consecutivos é constante</b>.</p>

Passo 2

<ol type=“a”>
<li>Segmentos paralelos às bases:</li>
<p>Base menor: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“5.333ex” height=“2.343ex” style=“vertical-align: -0.505ex;” viewBox=“0 -791.3 2295.9 1008.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> x + 3</title>
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<use xlink:href="#E1-MJMAIN-2B" x=“794” y=“0”></use>
<use xlink:href="#E1-MJMAIN-33" x=“1795” y=“0”></use>
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</svg></p>
<p>Segmento intermediário: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.495ex” height=“2.343ex” style=“vertical-align: -0.505ex;” viewBox=“0 -791.3 2796.4 1008.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 x + 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-78” d=“M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z”></path>
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<use xlink:href="#E1-MJMATHI-78" x=“500” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“1295” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“2295” y=“0”></use>
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<p>Base maior: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“6.495ex” height=“2.343ex” style=“vertical-align: -0.505ex;” viewBox=“0 -791.3 2796.4 1008.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 4 x - 3</title>
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<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
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<p>Como há três segmentos, o do meio é a média aritmética dos outros dois:</p>
<p style=“text-align:center;”></p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“27.684ex” height=“5.676ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1652.5 11919.4 2443.8” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 x + 2 = x + 3 + 4 x - 3 2 </title>
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<use xlink:href="#E1-MJMAIN-29" x=“3185” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-32" x=“3524” y="-687"></use>
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</svg></p>
<p style=“text-align:center;”></p>
<p>Simplificando:</p>
<p style=“text-align:center;”></p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“12.943ex” height=“10.176ex” style=“vertical-align: -4.505ex;” viewBox=“0 -2441.8 5572.8 4381.3” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 x + 2 = 5 x 2 4 x + 4 = 5 x x = 4 </title>
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<p style=“text-align:center;”></p>
<p style=“text-align:center;”></p>
<h1>Passo 3</h1>
<li>Segmentos paralelos às bases:</li>
<p>Base superior: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“5.158ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 2220.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> y + 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-79” d=“M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
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<use xlink:href="#E1-MJMAIN-2B" x=“719” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“1720” y=“0”></use>
</g>
</svg></p>
<p>Segmento médio: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.33ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 572.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> x</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-78” d=“M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-78" x=“0” y=“0”></use>
</g>
</svg></p>
<p>Base inferior: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“9.328ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 4016.4 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> x + y + 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-78” d=“M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-79” d=“M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
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<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
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<use xlink:href="#E1-MJMAIN-2B" x=“794” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-31" x=“3515” y=“0”></use>
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</svg></p>
<p>O segmento médio é a média aritmética das bases:</p>
<p style=“text-align:center;”></p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“25.178ex” height=“5.676ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1652.5 10840.4 2443.8” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> x = y + 2 + x + y + 1 2 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-78” d=“M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
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<path stroke-width=“1” id=“E1-MJMATHI-79” d=“M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
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<use xlink:href="#E1-MJMATHI-78" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“850” y=“0”></use>
<g transform=“translate(1628,0)”>
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<rect stroke=“none” width=“8693” height=“60” x=“0” y=“220”></rect>
<g transform=“translate(60,770)”>
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<g transform=“translate(389,0)”>
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<use xlink:href="#E1-MJMAIN-2B" x=“719” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-29" x=“2610” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“2999” y=“0”></use>
<g transform=“translate(3778,0)”>
<use xlink:href="#E1-MJMAIN-28" x=“0” y=“0”></use>
<g transform=“translate(389,0)”>
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<use xlink:href="#E1-MJMAIN-2B" x=“794” y=“0”></use>
<use xlink:href="#E1-MJMATHI-79" x=“1795” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“2515” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-29" x=“4405” y=“0”></use>
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<use xlink:href="#E1-MJMAIN-32" x=“4096” y="-687"></use>
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<p style=“text-align:center;”></p>
<p>Multiplicando por <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.162ex” height=“2.176ex” style=“vertical-align: -0.338ex;” viewBox=“0 -791.3 500.5 936.9” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMAIN-32" x=“0” y=“0”></use>
</g>
</svg>:</p>
<p style=“text-align:center;”></p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“25.861ex” height=“8.176ex” style=“vertical-align: -3.505ex;” viewBox=“0 -2011.3 11134.5 3520.2” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> 2 x = x + 2 y + 3 x = 2 y + 3  Equação  1 </title>
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<p>Agora analisamos o segmento inclinado interno, que divide proporcionalmente os lados congruentes. Isso implica que ele também divide a base proporcionalmente, logo:</p>
<p style=“text-align:center;”></p>
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<title> x = y  (Equação 2)</title>
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<text font-family=“monospace” stroke=“none” transform=“scale(71.759) matrix(1 0 0 -1 0 0)”>ã</text>
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<p style=“text-align:center;”></p>
<p>Substituindo em (1):</p>
<p style=“text-align:center;”></p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“18.989ex” height=“6.176ex” style=“vertical-align: -2.505ex;” viewBox=“0 -1580.7 8175.7 2659.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> y = 2 y + 3 y = - 3 ⇒ x = - 3 </title>
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<p style=“text-align:center;”></p>
<h1>Passo 4</h1>
<li>Segmentos paralelos às bases (de cima para baixo):</li>
<p style=“text-align:center;”></p>
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<title> 7 , x , y , 16 , z</title>
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<p>São <b>5 segmentos</b>, igualmente espaçados ⇒ formam uma <b>P.A.</b></p>
<p>A razão é:</p>
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<title> r = 16 - 7 3 = 3</title>
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<p style=“text-align:center;”></p>
<p>Agora calculamos os termos:</p>
<p style=“text-align:center;”></p>
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<title> x = 7 + 3 = 10 y = 10 + 3 = 13 z = 16 + 3 = 19 </title>
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<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“21.911ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 9434 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> x = 10 , y = 13 , z = 19</title>
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<path stroke-width=“1” id=“E1-MJMAIN-33” d=“M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-7A” d=“M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-39” d=“M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-78" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“850” y=“0”></use>
<g transform=“translate(1906,0)”>
<use xlink:href="#E1-MJMAIN-31"></use>
<use xlink:href="#E1-MJMAIN-30" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMAIN-2C" x=“2907” y=“0”></use>
<use xlink:href="#E1-MJMATHI-79" x=“3352” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“4128” y=“0”></use>
<g transform=“translate(5184,0)”>
<use xlink:href="#E1-MJMAIN-31"></use>
<use xlink:href="#E1-MJMAIN-33" x=“500” y=“0”></use>
</g>
<use xlink:href="#E1-MJMAIN-2C" x=“6185” y=“0”></use>
<use xlink:href="#E1-MJMATHI-7A" x=“6630” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“7376” y=“0”></use>
<g transform=“translate(8433,0)”>
<use xlink:href="#E1-MJMAIN-31"></use>
<use xlink:href="#E1-MJMAIN-39" x=“500” y=“0”></use>
</g>
</g>
</svg></p>
<p style=“text-align:center;”></p>
<li>Dados:</li>
</ol>
<p>Base maior: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.33ex” height=“1.676ex” style=“vertical-align: -0.338ex;” viewBox=“0 -576.1 572.5 721.6” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> x</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-78” d=“M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-78" x=“0” y=“0”></use>
</g>
</svg></p>
<p>Base menor: <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“1.155ex” height=“2.009ex” style=“vertical-align: -0.671ex;” viewBox=“0 -576.1 497.5 865.1” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> y</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-79” d=“M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-79" x=“0” y=“0”></use>
</g>
</svg></p>
<p>Segmento médio <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“18.095ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 7790.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> M N = x - 2 y + 5</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4D” d=“M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-3D” d=“M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-78” d=“M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2212” d=“M84 237T84 250T98 270H679Q694 262 694 250T679 230H98Q84 237 84 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-32” d=“M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-79” d=“M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-35” d=“M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-4D" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMATHI-4E" x=“1051” y=“0”></use>
<use xlink:href="#E1-MJMAIN-3D" x=“2217” y=“0”></use>
<use xlink:href="#E1-MJMATHI-78" x=“3274” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2212" x=“4068” y=“0”></use>
<use xlink:href="#E1-MJMAIN-32" x=“5069” y=“0”></use>
<use xlink:href="#E1-MJMATHI-79" x=“5570” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“6289” y=“0”></use>
<use xlink:href="#E1-MJMAIN-35" x=“7290” y=“0”></use>
</g>
</svg></p>
<p>Interseção das diagonais forma segmento <svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“5.158ex” height=“2.509ex” style=“vertical-align: -0.671ex;” viewBox=“0 -791.3 2220.9 1080.4” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> y + 1</title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-79” d=“M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-2B” d=“M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z”></path>
<path stroke-width=“1” id=“E1-MJMAIN-31” d=“M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z”></path>
</defs>
<g stroke=“currentColor” fill=“currentColor” stroke-width=“0” transform=“matrix(1 0 0 -1 0 0)” aria-hidden=“true”>
<use xlink:href="#E1-MJMATHI-79" x=“0” y=“0”></use>
<use xlink:href="#E1-MJMAIN-2B" x=“719” y=“0”></use>
<use xlink:href="#E1-MJMAIN-31" x=“1720” y=“0”></use>
</g>
</svg></p>
<p>📌 Propriedade importante</p>
<p>No trapézio, o segmento que liga os pontos médios dos lados não paralelos mede:</p>
<p style=“text-align:center;”><svg xmlns:xlink=“http://www.w3.org/1999/xlink” width=“14.042ex” height=“5.343ex” style=“vertical-align: -1.838ex;” viewBox=“0 -1508.9 6046 2300.3” role=“img” focusable=“false” xmlns=“http://www.w3.org/2000/svg” aria-labelledby=“MathJax-SVG-1-Title”>
<title> M N = B + b 2 </title>
<defs aria-hidden=“true”>
<path stroke-width=“1” id=“E1-MJMATHI-4D” d=“M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 154Q534 190 574 254T662 394Q837 673 839 675Q840 676 842 678T846 681L852 683H948Q965 683 988 683T1017 684Q1051 684 1051 673Q1051 668 1048 656T1045 643Q1041 637 1008 637Q968 636 957 634T939 623Q936 618 867 340T797 59Q797 55 798 54T805 50T822 48T855 46H886Q892 37 892 35Q892 19 885 5Q880 0 869 0Q864 0 828 1T736 2Q675 2 644 2T609 1Q592 1 592 11Q592 13 594 25Q598 41 602 43T625 46Q652 46 685 49Q699 52 704 61Q706 65 742 207T813 490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z”></path>
<path stroke-width=“1” id=“E1-MJMATHI-4E” d=“M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z”></path>
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<path stroke-width=“1” id=“E1-MJMATHI-42” d=“M231 637Q204 637 199 638T194 649Q194 676 205 682Q206 683 335 683Q594 683 608 681Q671 671 713 636T756 544Q756 480 698 429T565 360L555 357Q619 348 660 311T702 219Q702 146 630 78T453 1Q446 0 242 0Q42 0 39 2Q35 5 35 10Q35 17 37 24Q42 43 47 45Q51 46 62 46H68Q95 46 128 49Q142 52 147 61Q150 65 219 339T288 628Q288 635 231 637ZM649 544Q649 574 634 600T585 634Q578 636 493 637Q473 637 451 637T416 636H403Q388 635 384 626Q382 622 352 506Q352 503 351 500L320 374H401Q482 374 494 376Q554 386 601 434T649 544ZM595 229Q595 273 572 302T512 336Q506 337 429 337Q311 337 310 336Q310 334 293 263T258 122L240 52Q240 48 252 48T333 46Q422 46 429 47Q491 54 543 105T595 229Z”></path>
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<path stroke-width=“1” id=“E1-MJMATHI-62” d=“M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z”></path>
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<p>Logo:</p>
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<title> x - 2 y + 5 = x + y 2 </title>
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<p>Multiplicando por 2:</p>
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<title> 2 x - 4 y + 10 = x + y x = 5 y - 10  Equação  1 </title>
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<text font-family=“monospace” stroke=“none” transform=“scale(71.759) matrix(1 0 0 -1 0 0)”>ã</text>
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<p>Agora, a interseção das diagonais divide esse segmento médio na razão das bases. Como o desenho indica simetria:</p>
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<title> y + 1 = x 2 x = 2 y + 2   ( E q u a ç ã o   2   )   </title>
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<p>Igualando (1) e (2):</p>
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<title> 5 y - 10 = 2 y + 2 3 y = 12 y = 4 ⇒ x = 10 </title>
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<title> x = 10  e  y = 4</title>
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Resposta

<p>Ver o desenvolvimento </p>

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