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Giải bài 3.8 trang 34 sách bài tập toán 8 - Kết nối tri thức với cuộc sống

Chứng minh rằng trong hình thang có nhiều nhất hai góc tù.

𝄹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

Chứng minh rằng trong hình thang có nhiều nhất hai góc tù.

Phương pháp giải - Xem chi tiết

Sử dụng tính chất hai góc kề một đáy của hình thang có tổng bằng \(180^\circ \).

Lời giải chi tiết

Xét hình thang ABCD có AB // CDTa có:
  • \(\widehat A\) và \(\widehat D\) là hai góc kề với cạnh bên AD
Suy ra \(\widehat A + \widehat D = 180^\circ \) nên trong hai góc đó có nhiều nhất 1 góc tù.
  • \(\widehat B\) và \(\widehat C\) là hai góc kề với cạnh bên BC
Suy ra \(\widehat B + \widehat C = 180^\circ \) nên trong hai góc đó có nhiều nhất 1 góc tù.Do đó trong bốn góc \(\widehat A;\widehat B;\widehat C;\widehat D\)có nhiều nhất hai góc tù.

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