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Giải bài 9.13 trang 92 SGK Toán 8 tập 2 - Kết nối tri thức

Cho hình thang ABCD (AB // CD) có

🉐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

Cho hình thang ABCD (AB // CD) có \(\widehat {DAB} = \widehat {DBC}\)

a) Chứng minh rằng ΔABD ∽ ΔBDC 

b) Giả sử AB=2cm,AD=3cm,BD=4cm. Tính độ dài các cạnh BC và DC

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) Chứng minh ΔABD ∽ ΔBDC (g.g)

b) Tính tỉ số đồng dạng của tam giác ABD và tam giác BDC. Từ đó tính độ dài của DC, BC

Lời giải chi tiết

a) Có AB // CD Suy ra \(\widehat {AB{\rm{D}}} = \widehat {B{\rm{D}}C}\) - Xét  ΔABD và ΔBDC Có \(\widehat {AB{\rm{D}}} = \widehat {B{\rm{D}}C}{,^{}}\widehat {DAB} = \widehat {DBC}\)

Suy ra ΔABD ∽ ΔBDC (g.g)

b) Có \(\frac{{AB}}{{B{\rm{D}}}} = \frac{{12}}{{24}} = \frac{1}{2}\)

ΔABD ∽ ΔBDC với tỉ số \(\frac{1}{2}\)

Suy ra \(\frac{3}{{BC}} = \frac{4}{{DC}} = \frac{1}{2}\) Suy ra BC=6 (cm)      DC=8 (cm)

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