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Giải bài 4 trang 72 ôn tập chương sách bài tập toán 8 - Chân trời sáng tạo

Cho hình thang cân có độ dài hai đáy lần lượt là 10cm và 4cm, độ dài cạnh bên là 5cm. Hình thang đó có chiều cao là

꧅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

Cho hình thang cân có độ dài hai đáy lần lượt là 10cm và 4cm, độ dài cạnh bên là 5cm. Hình thang đó có chiều cao là A. 2cm. B. 3cm. C. 4cm. D. 6cm.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về định lí Pythagore vào tam giác vuông để tính: Trong một tam giác vuông, bình vuông độ dài của cạnh huyền bằng tổng các bình phương độ dài của hai cạnh góc vuông. 

Lời giải chi tiết

Vẽ hình thang cân ABCD có AB//CD, \(AB = 4cm,\) \(CD = 10cm\) và \(AD = BC = 5cm\)Kẻ \(AE \bot DC,BF \bot DC\left( {E,F \in DC} \right)\) nên \(\widehat {AED} = \widehat {AEF} = \widehat {BFE} = \widehat {BFC} = {90^0}\)Vì ABCD là hình thang cân nên \(\widehat D = \widehat C\)Tam giác AED và tam giác BFC có:\(\widehat {AED} = \widehat {BFC} = {90^0}\), \(\widehat D = \widehat C\), \(AD = BC = 5cm\)Do đó, \(\Delta AED = \Delta BFC\left( {ch - gn} \right)\). Suy ra \(DE = CF\)Tứ giác ABFE có: AB//EF, AE//BF (cùng vuông góc với DC) nên tứ giác ABFE là hình bình hành.Do đó, \(AB = FE = 4cm\)Suy ra: \(DE = FC = \frac{{DC - EF}}{2} = \frac{{10 - 4}}{2} = 3\left( {cm} \right)\)Áp dụng định lí Pythagore vào tam giác ADE vuông tại E có: \(A{E^2} = A{D^2} - D{E^2} = {5^2} - {3^2} = 16\), suy ra \(AE = 4cm\)Chọn C

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