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Giải bài 4.36 trang 65 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Cho AH và DK lần lượt là hai đường cao của hai tam giác ABC và DEF như Hình 4.38. Biết rằng

ꦛTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Cho AH và DK lần lượt là hai đường cao của hai tam giác ABC và DEF như Hình 4.38. Biết rằng \(\Delta ABC = \Delta DEF\). Hãy chứng minh AH = DK.

Phương pháp giải - Xem chi tiết

Chứng minh \(\Delta HAB = \Delta KDE\left( {ch - gn} \right)\)

Lời giải chi tiết

Ta có:\(\begin{array}{l}\Delta ABC = \Delta DEF\\ \Rightarrow \left\{ \begin{array}{l}AB = DE\\\widehat {ABC} = \widehat {DEF} hay \widehat {HBA} = \widehat {KED}\end{array} \right.\end{array}\)Xét \(\Delta HAB\) và \(\Delta KDE\) có:\(\widehat {AHB} = \widehat {DKE} = {90^0}\\AB = DE\\\widehat {HBA} = \widehat {KED}\left( {cmt} \right)\\ \Rightarrow \Delta HAB = \Delta KDE\left( {ch - gn} \right)\)\(\Rightarrow AH = DK\) (2 cạnh tương ứng)

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