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Giải Bài 9.5 trang 50 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Cho 2 đường thẳng song song c và d. Chứng minh rằng khoảng cách từ mọi điểm thuộc c đến đường thẳng d bằng nhau và bằng khoảng cách từ mọi điểm thuộc đường thẳng d đến đường thẳng c (khoảng cách đó được gọi là khoảng cách giữa hai đường thẳng song song c và d).

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

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

Cho 2 đường thẳng song song c và d. Chứng minh rằng khoảng cách từ mọi điểm thuộc c đến đường thẳng d bằng nhau và bằng khoảng cách từ mọi điểm  thuộc đường thẳng d đến đường thẳng c (khoảng cách đó được gọi là khoảng cách giữa hai đường thẳng song song c và d).

Phương pháp giải - Xem chi tiết

-Lấy M, M’ thuộc c (M khác M’), kẻ MH, M’H’ vuông góc với d. -Chứng minh: MH = H’M’ (\(\Delta MHH'\)=\(\Delta H'M'M\))

Lời giải chi tiết

Lấy M, M’ thuộc c (M khác M’), kẻ MH, M’H’ vuông góc với d.\( \Rightarrow MH\parallel M'H'\)Xét \(\Delta MHH'\) và \(\Delta H'M'M\)có:MH’: chung

\(\begin{array}{l}\widehat {{M_1}} = \widehat {H{'_2}}\left( {so\,le\,trong} \right)\\\widehat {{M_2}} = \widehat {H{'_1}}\left( {so\,le\,trong} \right)\\ \Rightarrow \Delta MHH' = \Delta H'M'M\left( {g - c - g} \right)\\ \Rightarrow MH = H'M'\end{array}\)
🃏 Vậy khoảng cách từ mọi điểm thuộc c đến đường thẳng d bằng nhau và bằng khoảng cách từ mọi điểm  thuộc đường thẳng d đến đường thẳng c. 

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