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Giải bài 3 trang 96 SGK Toán 7 tập 2 - Cánh diều

Cho tam giác ABC vuông cân tại A. Gọi M là trung điểm của cạnh huyền BC. Chứng minh tam giác MAB vuông cân.

♔Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Cho tam giác ABC vuông cân tại A. Gọi M là trung điểm của cạnh huyền BC. Chứng minh tam giác MAB vuông cân.

Phương pháp giải - Xem chi tiết

Ta chứng minh tam giác MAB 🎶vuông cân bằng cách chứng minh trong tam giác có một góc vuông tại một đỉnh và có cặp cạnh bằng nhau xuất phát từ đỉnh đó.

Lời giải chi tiết

Tam giác ABC vuông cân tại A nên \(\widehat A = 90^\circ ;\widehat B = \widehat C; AB = AC\).

Tổng ba góc trong một tam giác bằng 180° nên \(\widehat B = \widehat C = 90:2 = 45^\circ \).

Xét tam giác ABM và tam giác ACM có:

AB = AC

AM chung BM = CM \(\Rightarrow \Delta ABM = \Delta ACM\) (c.c.c) \(\Rightarrow \widehat {BAM} = \widehat {CAM}\) (2 góc tương ứng) Mà \(\widehat {BAM} + \widehat {CAM}=\widehat{BAC}=90^0\) \(\Rightarrow \widehat {BAM} = \widehat {CAM} = 90:2 = 45^\circ \).

Xét tam giác MAB༺: \(\widehat {MBA} = \widehat {BAM} = 45^\circ  \Rightarrow \widehat {BMA} = 90^\circ ;MB = MA\).

Vậy tam giác MAB vuông cân tại M.

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Tham Gia Group Dành Cho Lớp 7 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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