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Giải bài 6 trang 67 SGK Toán 8 – Chân trời sáng tạo

Ta gọi tứ giác ABCD với

💖Tổng 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

Ta gọi tứ giác ABCD với AB = AD, CB = CD (hình 13) là hình “cái diều”. a. Chứng minh rằng AC là đường trung trực của BD.

⛦b. Cho biết \(\widehat B = {95^0},\widehat C = {35^0}.\)Tính \(\widehat A\) và \(\widehat D\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

🔯a) Sử dụng tính chất của đường trung trực để chứng minh \(AC\) là trung trực của \(BD\)

b) Sử dụng tính chất tổng bốn góc trong tứ giác \(ABCD\)

Lời giải chi tiết

a) Ta có:

✱\(AB = AD\) (gt) nên \(A\) thuộc đường trung trực của \(BD\)

💦\(CB = CD\) (gt) nên \(C\) thuộc đường trung trực của \(BD\)

Vậy \(AC\) là đường trung trực của \(BD\)

b) Xét \(\Delta ABC\) và \(\Delta ADC\) ta có:

\(AB = AD\) (gt)

\(BC = CD\) (gt)

\(AC\) chung

Suy ra: \(\Delta ABC = \Delta ADC\) (c-c-c)

🦩Suy ra: \(\widehat {ABC} = \widehat {ADC} = 95^\circ \) (hai góc tương ứng)

🍸Trong tứ giác \(ABCD\), tổng các góc bằng \(360^\circ \) nên:

🐷\(\widehat A = 360^\circ  - \left( {95^\circ  + 35^\circ  + 95^\circ } \right) = 135^\circ \)

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