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Giải bài 2 trang 68 sách bài tập toán 8 - Chân trời sáng tạo tập 2

Quan sát Hình 6, chứng minh rằng: a) $\Delta MNP\backsim \Delta DPC$. b) $NP\bot PC$.

ཧTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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

Quan sát Hình 6, chứng minh rằng: a) $\Delta MNP\backsim \Delta DPC$. b) $NP\bot PC$.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về áp dụng các trường hợp đồng dạng của tam giác vào tam giác vuông: Nếu cạnh huyền và một cạnh góc vuông của tam giác vuông này tỉ lệ với cạnh huyền và một cạnh góc vuông của tam giác vuông kia thì hai tam giác vuông đó đồng dạng với nhau.

Lời giải chi tiết

a) Tam giác MNP và tam giác DPC có: $\widehat{M}=\widehat{PDC}={{90}^{0}},\frac{NM}{DP}=\frac{NP}{PC}\left( =\frac{3}{2} \right)$Do đó, $\Delta MNP\backsim \Delta DPC\left( ch-cgv \right)$b) Vì $\Delta MNP\backsim \Delta DPC\left( cmt \right)$ nên $\widehat{NPM}=\widehat{C}$Mà $\widehat{C}+\widehat{DPC}={{90}^{0}}$ nên $\widehat{NPM}+\widehat{DPC}={{90}^{0}}$, hay $\widehat{NPC}={{90}^{0}}$. Do đó, $NP\bot PC$.

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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