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Giải bài 5 trang 91 vở thực hành Toán 8 tập 2

Cho các điểm A, B, C, D, E như Hình 9.30. Biết rằng \(\widehat{BAC}=\widehat{CDB}\). Chứng minh rằng ΔAED ∽ ΔBEC.

♕Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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

𒐪Cho các điểm A, B, C, D, E như Hình 9.30. Biết rằng \(\widehat{BAC}=\widehat{CDB}\). Chứng minh rằng ΔAED ∽ ΔBEC.

Phương pháp giải - Xem chi tiết

ജ- Chứng minh ΔAEB ∽ ΔDEC  suy ra: \(\frac{A\text{E}}{DE}=\frac{BE}{CE}\Rightarrow \frac{A\text{E}}{BE}=\frac{DE}{CF}\)

- Chứng minh ΔAED ∽ ΔBEC (c.g.c)

Lời giải chi tiết

Hai tam giác AEB và DEC có: $\widehat{AEB}=\widehat{DEC}$(hai góc đối đỉnh), $\widehat{BAC}=\widehat{CDB}$ (theo giả thiết).Vậy $\Delta AEB\backsim \Delta DEC$ (g.g). Suy ra $\frac{EA}{ED}=\frac{EB}{EC}$, hay $\frac{EA}{EB}=\frac{ED}{EC}$.

Hai tam giác AED và BEC có: $\frac{EA}{EB}=\frac{ED}{EC}$ (theo chứng minh trên); $\widehat{AED}=\widehat{BEC}$ (hai góc đối đỉnh). Vậy ΔAED ∽ ΔBEC (c.g.c).

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

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