Cho tam giác ABC có 3 góc nhọn. Vẽ ra phía ngoài tam giác các hình vuông ABDE và ACFH:
a, Chứng minh EC=BH
b. Chứng minh EC vuông góc với BH
K
Khách
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NL
Nguyễn Lê Khánh Linh
29 tháng 12 2020
Hok tốt nha
Các bn nhớ t cho mk ná
Đúng(1)
Những câu hỏi liên quan
5 tháng 8 2017
Cho tam giác ABC.Vẽ về phía ngoài tam giác các hình vuông ABDE và ACFG có tâm theo thứ tự là M,N.Gọi I,K theo thứ tự là trung điểm của EG,BC. - Hình học - Diễn đàn Toán học
9 tháng 12 2018
Đề bị sai từ câu đầu tiên. Tam giác chỉ có thể kí hiệu bằng 3 chữ cái in hoa.
PT
1
CM
30 tháng 3 2018
Ta có: ∠ (BAH) = ∠ (BAC) + ∠ (CAH) = ∠ (BAC) + 90 0
∠ (EAC) = ∠ (BAC) + ∠ (BAE) = ∠ (BAC) + 90 0
Suy ra: ∠ (BAH) = ∠ (EAC)
* Xét ∆ BAH và ∆ EAC , ta có:
BA = EA (vì ABDE là hình vuông)
∠ (BAH) = ∠ (EAC) (chứng minh trên)
AH = AC (vì ACFH là hình vuông)
Suy ra: ∆ BAH = ∆ EAC (c.g.c) ⇒ BH = EC
Gọi K và O lần lượt là giao điểm của EC với AB và BH.
Ta có: ∠ (AEC) = ∠ (ABH) (vì ∆ BAH = ∆ EAC) (1)
Hay ∠ (AEK) = ∠ (OBK)
* Trong ∆ AEK, ta có: ∠ (EAK) = 90 0
⇒ ∠ (AEK) + ∠ (AKE) = 90 0 (2)
Mà ∠ (AKE) = ∠ (OKB) (đối đỉnh) (3)
Từ (1), (2) và (3) suy ra:
∠ (OKB) + ∠ (OBK) = 90 0
* Trong Δ BOK ta có:
∠ (BOK) + ∠ (OKB) + ∠ (OBK) = 180 0
⇒ ∠ (BOK) = 180 0 – ( ∠ (OKB) + ∠ (OBK) ) = 180 0 – 90 0 = 90 0
Suy ra: EC ⊥ BH
19 tháng 12 2019
1. ABDE là hình vuông (gt) => AE = AB (Đn) (1)
ACFH là hình vuông (gt) => AC = AH (đn) (2)
góc HAC = góc EAB = 90 do ...
góc HAC + góc BAC = góc BAH
góc EAB + góc BAC = EAC
=> góc EAC = góc BAH ; (1)(2)
=> tam giác EAC = tam giác BAH (c-g-c)
15 tháng 6 2022
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