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Giải bài 9.24 trang 76 SGK Toán 7 tập 2 - Kết nối tri thức

Gọi BE và CF là hai đường phân giác của tam giác ABC cân tại A. Chứng minh BE = CF.

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

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Đề bài

Gọi BE và CF là hai đường phân giác của tam giác ABC cân tại A. Chứng minh BE = CF.

Phương pháp giải - Xem chi tiết

Sử dụng tính chất của tam giác cân, xét 2 tam giác bằng nhau rồi chỉ ra 2 cạnh tương ứng bằng nhau.

Lời giải chi tiết

Vì tam giác ABC cân tại A nên AB = AC; \(\widehat {ABC} = \widehat {ACB}\) ( tính chất)Vì BE là là tia phân giác của góc ABC nên \(\widehat {{B_1}} = \widehat {{B_2}} = \dfrac{1}{2}.\widehat {ABC}\)Vì CF là tia phân giác của góc ACB nên \(\widehat {{C_1}} = \widehat {{C_2}} = \dfrac{1}{2}.\widehat {ACB}\)Do đó, \(\widehat {{B_1}} = \widehat {{C_1}}\)Xét \(\Delta ABE\) và \(\Delta ACF\), ta có:\(\widehat A\) chungAB = AC\(\widehat {{B_1}} = \widehat {{C_1}}\)\( \Rightarrow \Delta ABE = \Delta ACF\left( {g.c.g} \right)\)\( \Rightarrow \)BE = CF ( 2 cạnh tương ứng)

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