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Matematyka i przykłady jej zastosowań 2. Zakres podstawowy. Reforma 2019

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<table style="height:17px;width:100%;border-collapse:collapse;background-color:#dcdcdc;" border="0"> <tbody> <tr style="height:17px;"> <td style="width:100%;height:17px;"> Równanie prostej AB, gdy A=(xA, yA), B=(xB, yB) i xA≠xB, ma postać: (y−yA​)(xB​−xA​)−(yB​−yA​)(x−xA​)=0 &nbsp; </td> </tr> </tbody> </table> <hr> a) Rysunek pomocniczy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/132970/cOavLh6UNyOFgA33BJkDww%3D%3D_cd74676851749e707938b434c27da3e6306158e447b1a89a94201b73b2824d6d.jpg" alt="" width="493" height="493">

<table style="height:17px;width:100%;border-collapse:collapse;background-color:#dcdcdc;" border="0"> <tbody> <tr style="height:17px;"> <td style="width:100%;height:17px;"> Równanie prostej AB, gdy A=(xA, yA), B=(xB, yB) i xA≠xB, ma postać: (y−yA​)(xB​−xA​)−(yB​−yA​)(x−xA​)=0 &nbsp; </td> </tr> </tbody> </table> <hr> Rysunek poglądowy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/132976/vZlieDRW/GpMkiVoSzPs2w%3D%3D_8415ee89510d314e1ba2e3e72c3b3628a39c40935a2aed8abfdc01be9fe52feb.jpg" alt="" width="424" height="425">

<table style="width:688px;border-collapse:collapse;background-color:#dcdcdc;height:82px;" border="0"> <tbody> <tr> <td style="width:683.466px;"> Prosta o współczynniku kierunkowym a przechodząca przez punkt A=(xA, yA) ma równanie: y−yA​=a(x−xA​) &nbsp; </td> </tr> </tbody> </table> <hr> a) Podstawiamy współrzędne punktu A i współczynnik a do równania w ramce i wyznaczamy równanie prostej w postaci kierunkowej: y−yA​=a(x−xA​) &nbsp; y−6=3(x−2) &nbsp;

<table style="height:17px;width:100%;border-collapse:collapse;background-color:#dcdcdc;" border="0"> <tbody> <tr style="height:17px;"> <td style="width:100%;height:17px;"> Równanie prostej AB, gdy A=(xA, yA), B=(xB, yB) i xA≠xB, ma postać: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e48eb2bbd18b6175bfebb75496240e78cd685c00a15d8b28d35ffde49336ff9b_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e48eb2bbd18b6175bfebb75496240e78cd685c00a15d8b28d35ffde49336ff9b_big.svg" type="image/svg+xml"></object> &nbsp; </td> </tr> </tbody> </table> <hr> a) Rysunek pomocniczy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/132970/cOavLh6UNyOFgA33BJkDww%3D%3D_cd74676851749e707938b434c27da3e6306158e447b1a89a94201b73b2824d6d.jpg" alt="" width="493" height="493">

<table style="height:17px;width:100%;border-collapse:collapse;background-color:#dcdcdc;" border="0"> <tbody> <tr style="height:17px;"> <td style="width:100%;height:17px;"> Równanie prostej AB, gdy A=(xA, yA), B=(xB, yB) i xA≠xB, ma postać: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e48eb2bbd18b6175bfebb75496240e78cd685c00a15d8b28d35ffde49336ff9b_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e48eb2bbd18b6175bfebb75496240e78cd685c00a15d8b28d35ffde49336ff9b_big.svg" type="image/svg+xml"></object> &nbsp; </td> </tr> </tbody> </table> <hr> Rysunek poglądowy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/132976/vZlieDRW/GpMkiVoSzPs2w%3D%3D_8415ee89510d314e1ba2e3e72c3b3628a39c40935a2aed8abfdc01be9fe52feb.jpg" alt="" width="424" height="425">

<table style="width:688px;border-collapse:collapse;background-color:#dcdcdc;height:82px;" border="0"> <tbody> <tr> <td style="width:683.466px;"> Prosta o współczynniku kierunkowym a przechodząca przez punkt A=(xA, yA) ma równanie: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f6c93b8ac755fa83205acaf9662ec574206431b19ba47ec3672513091b9b23c6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f6c93b8ac755fa83205acaf9662ec574206431b19ba47ec3672513091b9b23c6_big.svg" type="image/svg+xml"></object> &nbsp; </td> </tr> </tbody> </table> <hr> a) Podstawiamy współrzędne punktu A i współczynnik a do równania w ramce i wyznaczamy równanie prostej w postaci kierunkowej: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f6c93b8ac755fa83205acaf9662ec574206431b19ba47ec3672513091b9b23c6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f6c93b8ac755fa83205acaf9662ec574206431b19ba47ec3672513091b9b23c6_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/ab25574f1758a8b8b78cab05544f1c07c4a795e3132ad7285066389b5c09ef63_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/ab25574f1758a8b8b78cab05544f1c07c4a795e3132ad7285066389b5c09ef63_big.svg" type="image/svg+xml"></object> &nbsp;

<table style="height:17px;width:100%;border-collapse:collapse;background-color:#dcdcdc;" border="0"> <tbody> <tr style="height:17px;"> <td style="width:100%;height:17px;"> Równanie prostej AB, gdy A=(xA, yA), B=(xB, yB) i xA≠xB, ma postać: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e48eb2bbd18b6175bfebb75496240e78cd685c00a15d8b28d35ffde49336ff9b_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e48eb2bbd18b6175bfebb75496240e78cd685c00a15d8b28d35ffde49336ff9b_big.svg" type="image/svg+xml"></object> &nbsp; </td> </tr> </tbody> </table> <hr> Punkty A i B leżą symetrycznie względem osi y, więc możemy założyć, że: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/50c83efd0bed0dcf3df816023d1b164029f76a6bfd6e8288440edc3cf44fcd1d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/50c83efd0bed0dcf3df816023d1b164029f76a6bfd6e8288440edc3cf44fcd1d_big.svg" type="image/svg+xml"></object> &nbsp; <hr> Przyjmijmy oznaczenia jak na rysunku poniżej: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/132994/7fHe0uMz/P59zswUA7/DcQ%3D%3D_872b8c0b2abcd588fa9cdc72815d212f29dbfe427f7c301e57f8cb60b34b8168.jpg" alt="" width="510" height="515"> <hr> Obliczamy długość boku trójkąta równobocznego: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/749cfa1cbbf57a3d17582b55aa1795123b69c75579244073293437a43b125699_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/749cfa1cbbf57a3d17582b55aa1795123b69c75579244073293437a43b125699_big.svg" type="image/svg+xml"></object> &nbsp; Ze wzoru na wysokość trójkąta równobocznego: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8ab155070adf6bfacade80f64dac802e75a0e92b53f20d0ac1ec6d07c2505616_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8ab155070adf6bfacade80f64dac802e75a0e92b53f20d0ac1ec6d07c2505616_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; Bok AB trójkąta leży na osi x, więc prosta AB ma równanie: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c49641d768f5b8cbcc21a5240d08377e53cb8f8901b935eb2f91cd7ac670a0f7_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c49641d768f5b8cbcc21a5240d08377e53cb8f8901b935eb2f91cd7ac670a0f7_big.svg" type="image/svg+xml"></object> &nbsp; <hr> Punkt C może leżeć powyżej lub poniżej osi x, więc rozważymy dwa przypadki. <hr> Przypadek I: Punkt C=C1 leży powyżej osi x. Wówczas: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/3be65ef0e540748839729af2f04e80b9ad0a5daca0d71f4af6c15956fd1efcff_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/3be65ef0e540748839729af2f04e80b9ad0a5daca0d71f4af6c15956fd1efcff_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/88c41d1500e35a96de8508fb8be936488d7ea8e5603e793426f660fe09d6c7f9_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/88c41d1500e35a96de8508fb8be936488d7ea8e5603e793426f660fe09d6c7f9_big.svg" type="image/svg+xml"></object> &nbsp; Podstawiamy współrzędne punktu C=C1 do równania w ramce i wyznaczamy równanie prostej AC1 w postaci kierunkowej: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/54e16fcafc95418716018242ec62c3684f6731d2d4ff0cd724c95f9b25ce9626_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/54e16fcafc95418716018242ec62c3684f6731d2d4ff0cd724c95f9b25ce9626_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/17120a4ba3d147cbdcb09fe871d823e4e3b0820450174b9e30bca6ac06be7de3_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/17120a4ba3d147cbdcb09fe871d823e4e3b0820450174b9e30bca6ac06be7de3_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7f2375d7bc1e11755d41de73742ae9b26f0da6ab5371f594bb801e70d03215bd_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7f2375d7bc1e11755d41de73742ae9b26f0da6ab5371f594bb801e70d03215bd_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/d80186a3737724456e634bfaf52900958806094e26f9a1c417fe8779d4481cc1_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/d80186a3737724456e634bfaf52900958806094e26f9a1c417fe8779d4481cc1_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8633c1167957d464f821106de76c40796fd503774d01177d20666d30600d282c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8633c1167957d464f821106de76c40796fd503774d01177d20666d30600d282c_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/89ee40478be4c16c18f0a95c67a6fcab14fea1431248d62c529b653aae16a6eb_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/89ee40478be4c16c18f0a95c67a6fcab14fea1431248d62c529b653aae16a6eb_big.svg" type="image/svg+xml"></object> &nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/96cbd0f85c801ce8ea052707580776b90ff3c55ef8c4bca1d08137113dba7650_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/96cbd0f85c801ce8ea052707580776b90ff3c55ef8c4bca1d08137113dba7650_big.svg" type="image/svg+xml"></object> &nbsp; Podstawiamy współrzędne punktu C=C1 do równania w ramce i wyznaczamy równanie prostej BC1 w postaci kierunkowej: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/160e92e5ff4661475482493512c84601187c843190c0e13d72a35371989db1bb_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/160e92e5ff4661475482493512c84601187c843190c0e13d72a35371989db1bb_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/814321fc8027d6c288d7f9c3f8fa0c40125df72ce4f325cc5a0b0054b986ed89_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/814321fc8027d6c288d7f9c3f8fa0c40125df72ce4f325cc5a0b0054b986ed89_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/ad0eb81e7680a0ab5b39e766db00982396cdac61c213755495f5c776ed4b4910_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/ad0eb81e7680a0ab5b39e766db00982396cdac61c213755495f5c776ed4b4910_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0632b7fa604a7165d194e66c144b7c42ef770f003a6903a32d67233ee565bb0d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0632b7fa604a7165d194e66c144b7c42ef770f003a6903a32d67233ee565bb0d_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/667e67a37de5b14b7d9a766e8eeb0c433189d734883d70226575657d8e5b8833_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/667e67a37de5b14b7d9a766e8eeb0c433189d734883d70226575657d8e5b8833_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/87afacf7d80b84970610c8ff61b4039d707bb2ca91821254fd4385f5ba21b1d0_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/87afacf7d80b84970610c8ff61b4039d707bb2ca91821254fd4385f5ba21b1d0_big.svg" type="image/svg+xml"></object> &nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/22ee5760bcc7ff2c88316183db4ce94b9fed0a4ed7c9bf321669a755c54b0856_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/22ee5760bcc7ff2c88316183db4ce94b9fed0a4ed7c9bf321669a755c54b0856_big.svg" type="image/svg+xml"></object> &nbsp; <hr> Przypadek II: Punkt C=C2 leży poniżej osi x. Wówczas: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4651ec1701c497df38343df115ac157b5d53ce200635dffa80fd498d927ea464_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4651ec1701c497df38343df115ac157b5d53ce200635dffa80fd498d927ea464_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/3437cac09ee1fc2989de8fdaaccc43e2ff9af8727c5f9480c80546f8d525e854_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/3437cac09ee1fc2989de8fdaaccc43e2ff9af8727c5f9480c80546f8d525e854_big.svg" type="image/svg+xml"></object> &nbsp; Podstawiamy współrzędne punktu C=C2 do równania w ramce i wyznaczamy równanie prostej AC2 w postaci kierunkowej: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/54e16fcafc95418716018242ec62c3684f6731d2d4ff0cd724c95f9b25ce9626_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/54e16fcafc95418716018242ec62c3684f6731d2d4ff0cd724c95f9b25ce9626_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/9a1fc296d14e0240e2e0190dccb194ada03a1b69743ad5947fc515570262627b_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/9a1fc296d14e0240e2e0190dccb194ada03a1b69743ad5947fc515570262627b_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0ab9d2c5491bbab62381ff25018332469694eb5060c6f1f067e93815043f63ff_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0ab9d2c5491bbab62381ff25018332469694eb5060c6f1f067e93815043f63ff_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7abb9b019c048f635c5761cdec641e314e095de05519f937a7bd15a95030b85e_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7abb9b019c048f635c5761cdec641e314e095de05519f937a7bd15a95030b85e_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/ad342ffb7a579c65595578a1f1b9438f03beaa8c066a83403089ea898752d22c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/ad342ffb7a579c65595578a1f1b9438f03beaa8c066a83403089ea898752d22c_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/85e7cd8b00cdc200233f8d5d7ab002489758a2aee664ed2594034e4ae21e9409_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/85e7cd8b00cdc200233f8d5d7ab002489758a2aee664ed2594034e4ae21e9409_big.svg" type="image/svg+xml"></object> &nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/07690299d5e927c3a8718d789e6f7afee6f2ae013eddf7cf48c5f132eef1ec83_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/07690299d5e927c3a8718d789e6f7afee6f2ae013eddf7cf48c5f132eef1ec83_big.svg" type="image/svg+xml"></object> &nbsp; Podstawiamy współrzędne punktu C=C1 do równania w ramce i wyznaczamy równanie prostej BC1 w postaci kierunkowej: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/160e92e5ff4661475482493512c84601187c843190c0e13d72a35371989db1bb_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/160e92e5ff4661475482493512c84601187c843190c0e13d72a35371989db1bb_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/9cd34353ec111dfd3dbf2ea8c363635738d913a547f7a2b2796a0ceb1655b299_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/9cd34353ec111dfd3dbf2ea8c363635738d913a547f7a2b2796a0ceb1655b299_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0f3f463aab63b60fff75e81770f97d6238925bf3d432545908244493bac54a10_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0f3f463aab63b60fff75e81770f97d6238925bf3d432545908244493bac54a10_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/923355fd6aec34795a3a467f1b0cdde3cb66f3fd04e5bda58cc3a705de4643f4_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/923355fd6aec34795a3a467f1b0cdde3cb66f3fd04e5bda58cc3a705de4643f4_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/805a090cb6ba3d068b4c64231478792d6494351d34b3ac8b60b486bdad6d4313_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/805a090cb6ba3d068b4c64231478792d6494351d34b3ac8b60b486bdad6d4313_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/384c653ca858da668c74965f641b89e4c88ae48076603347c2a972751f28399b_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/384c653ca858da668c74965f641b89e4c88ae48076603347c2a972751f28399b_big.svg" type="image/svg+xml"></object> &nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c3e2dcc8e81c76e0e93bcd788c1ffa845d124da63a9fdde61fab8e1b06a844bf_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c3e2dcc8e81c76e0e93bcd788c1ffa845d124da63a9fdde61fab8e1b06a844bf_big.svg" type="image/svg+xml"></object> &nbsp; <hr> Odp. Boki trójkąta zawierają się w prostych: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/dab9e1e2369ba397b6b4514010cb12a45069a0650c355d2c0ee173f1238ddec3_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/dab9e1e2369ba397b6b4514010cb12a45069a0650c355d2c0ee173f1238ddec3_big.svg" type="image/svg+xml"></object> &nbsp; lub <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7e2582cc04545089598b8912f876314eb16ed1c44cccc7fb5f679ca500ee51fe_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7e2582cc04545089598b8912f876314eb16ed1c44cccc7fb5f679ca500ee51fe_big.svg" type="image/svg+xml"></object> &nbsp;

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