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Giải bài 3 trang 90 vở thực hành Toán 8 tập 2

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

ౠTổng 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.

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) Hai tam giác ABD và BDC có: $\widehat{ABD}=\widehat{BDC}$ (hai góc so le trong), $\widehat{DAB}=\widehat{CBD}$ (theo giả thiết).Do đó $\Delta ABD\backsim \Delta BDC$ (g.g).b) Từ $\Delta ABD\backsim \Delta BDC$ suy ra $\frac{AD}{BC}=\frac{BD}{DC}=\frac{AB}{BD}=\frac{1}{2}$.Do đó BC = 2.AD = 6 (cm), DC = 2.BD = 8 (cm)

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