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Giải bài 5 trang 49 vở thực hành Toán 8

Cho hình thang cân ABCD có đáy nhỏ BC. Hạ BH ⊥ AD, CE ⊥ AD.

🌞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 cân ABCD có đáy nhỏ BC. Hạ BH ⊥ AD, CE ⊥ AD. a) Chứng minh AH = ED. b) Cho BH = 4 cm, và \(\widehat A = 45^\circ .\) Tính độ dài ED.

Phương pháp giải - Xem chi tiết

🗹a) Dựa vào tính chất của hình thang cân và chứng minh \(\Delta ABH = \Delta DCE\) suy ra AH = ED (hai cạnh tương ứng).

♑b) Chứng minh tam giác ABH vuông cân tại H suy ra độ dài các cạnh tương ứng, ta tính được độ dài ED.

Lời giải chi tiết

ꩲa) Ta có hình thang ABCD cân nên \(\widehat D = \widehat A,AB = CD\).

𝔍Xét hai tam giác vuông ABH và DCE có: \(\widehat D = \widehat A,AB = CD\), do đó \(\Delta ABH = \Delta DCE\) (cạnh huyền – góc nhọn). Từ đó suy ra AH = ED.

🙈b) Ta có \(\widehat A = {45^0},BH \bot AD\) nên tam giác ABH vuông cân tại H.

𓄧\( \Rightarrow AH = BH\) mà \(AH = ED \Rightarrow ED = BH = 4cm\) (chứng minh trên).

Vậy ED = 4 cm.

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