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Giải bài 3.26 trang 75 SGK Toán 8 - Cùng khám phá

Cho hình thang ABCD có
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Đề bài

Cho hình thang ABCD có \(\widehat A = \widehat D = {90^0},AB = 3cm,AD = 4cm\) và \(CD = 6cm\)(hình 3.64). Tính độ dài cạnh BC.

 

Phương pháp giải - Xem chi tiết

Kẻ \(BH \bot DC\) Sử dụng tính chất trong hình chữ nhật: Các cạnh đối song song và bằng nhau. Hai đường chéo bằng nhau và cắt nhau tại trung điểm của mỗi đường.

Lời giải chi tiết

Kẻ \(BH \bot DC\)Xét tứ giác ABHC có \(\widehat A = \widehat H = \widehat D = 90^\circ \) suy ra ABHD là hình chữ nhật \( \Rightarrow AD = BH = 4cm;AB = DH = 3cm.\)\( \Rightarrow CH = CD - DH = 3cm.\)Xét tam giác vuông \(BHC\) có \(B{H^2} + H{C^2} = B{C^2}\) (định lí Pythagore)\( \Rightarrow BC = \sqrt {B{H^2} + H{C^2}}  = 5cm.\)

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