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Giải bài 4 trang 71 vở thực hành Toán 7

Bài 4. Cho hình vẽ bên. Biết \(\widehat {DAC} = \widehat {CBD} = {90^o},AD = BC\), hãy chứng minh rằng \(\widehat {BAD} = \widehat {ABC}\).

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

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Đề bài

Bàiꦦ 4. Cho hình vẽ bên. Biết \(\widehat {DAC} = \widehat {CBD} = {90^o},AD = BC\), hãy chứng minh rằng \(\widehat {BAD} = \widehat {ABC}\).

Phương pháp giải - Xem chi tiết

Chứng minh tam giác BAD và ABC bằng nhau.

Lời giải chi tiết

Ta thấy hai tam giác ADC và BCD lần lượt vuông góc tại các đỉnh A, B và có:DC là cạnh chungAD = BC (theo giả thiết)Vậy \(\Delta ADC = \Delta BCD\)(cạnh huyền – cạnh góc vuông). Từ đây suy ra AC = BD.Hai tam giác BAD và ABC có: AD = BC (theo giả thiết), AB là cạnh chung, BD = AC (theo chứng minh trên). Vậy \(\Delta BAD = \Delta ABC\)(hai cạnh góc vuông).Suy ra \(\widehat {BAD} = \widehat {ABC}\).

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