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Giải bài 2 trang 63 vở thực hành Toán 8

Cho hình bình hành ABCD. Các tia phân giác của góc A, B, C, D cắt nhau như trên Hình 3.39.

🌸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 bình hành ABCD. Các tia phân giác của góc A, B, C, D cắt nhau như trên Hình 3.39.

 

Chứng minh rằng EFGH là hình chữ nhật.

Phương pháp giải - Xem chi tiết

Chứng minh ba góc của tứ giác EFGH là góc vuông.

Lời giải chi tiết

Ta sẽ chứng minh ba góc của tứ giác EFGH là góc vuông.

🐽Xét tam giác ECD có: \(\widehat {ECD} = \frac{1}{2}\widehat {BCD}\) (do EC là đường phân giác của \(\widehat {BCD}\)),

𓃲\(\widehat {EDC} = \frac{1}{2}\widehat {ADB}\) (do ED là đường phân giác của \(\widehat {ADB}\)), mà \(\widehat {BCD} + \widehat {ADC} = 180^\circ \) nên \(\widehat {ECD} + \widehat {EDC} = 90^\circ \).

Từ đó, tam giác ECD vuông tại E.Tương tự, chứng minh được tam giác FBC vuông tại F, tam giác AHD vuông tại H. Tứ giác EFGH có ba góc vuông nên là hình chữ nhật.

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