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Giải bài 2 (4.24) trang 73 vở thực hành Toán 7

Bài 2 (4.24). Cho tam giác ABC cân tại A và M là trung điểm của BC. Chứng minh AM vuông góc với BC và AM là tia phân giác của góc BAC.

ꦑTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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Đề bài

Bài💯 2 (4.24). Cho tam giác ABC cân tại A và M là trung điểm của BC. Chứng minh AM vuông góc với BC và AM là tia phân giác của góc BAC.

Phương pháp giải - Xem chi tiết

Chứng minh \(\widehat {AMB} = {90^o}\) và AM là tia phân giác của góc BAC .

Lời giải chi tiết

GT \(\Delta ABC\)cân tại A, \(M \in BC,MB = MC.\)
KL  \(AM \bot BC,\widehat {MAB} = \widehat {MAC}\)
Xét tam giác ABM và ACM ta có:AB = AC (do \(\Delta ABC\)cân tại A)\(\widehat {ABM} = \widehat {ACM}\) (do \(\Delta ABC\)cân tại A)MB = MC (theo giả thiết)Vậy \(\Delta ABM = \Delta ACM\)(c – g – c). Do đó \(\widehat {MAB} = \widehat {MAC}\) hay AM là tia phân giác của góc BAC.Đồng thời  \(\widehat {AMB} = \widehat {AMC} = \frac{{\widehat {AMB} + \widehat {AMC}}}{2} = \frac{{{{180}^o}}}{2} = {90^o}\) hay \(AM \bot BC.\)

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