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Function: require_once
수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
△π
2020.06.27 03:39
조회 719
(1)사다리 모양으로 사다리꼴(????) 3개가 있다. 이때, 각각의 사다리꼴의 높이는 같다. 이제, 각각의 사다리꼴의 대각선을 모두 그으면, 가로로 퍼진 모양의 둔각삼각형이 6개 보일 것이다.
이 때, 맨 위에 있는 삼각형과 맨 아래에 있는 삼각형의 합은, 위에서 두 번째에 있는 삼각형과 아래에서 두 번째에 있는 삼각형의 합임을 보여라.
(2)이제, 이를 서로 닮은 사각형(사다리꼴이 아니어도 됨) 3개로 일반화시키자. 이때도 실제로 위 증명 내용이 성립한다!!! 이를 증명하여라.
(수정:(2) 문제를 다음과 같이 수정합니다.
일반사각형 ABCD가 있다. AB의 중점인 M과 CD의 중점인 N이 있을 때, DM, AN의 교점을 G, CM, BN의 교점을 H이라 할 때, 삼각형 ADH와 삼각형 BCH의 합은 사각형 HNGM임을 보여시오.)
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파스칼
Lv.7
2020.06.28 09:56
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△π
Lv.9
2020.06.28 16:47
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파스칼
Lv.7
2020.06.28 17:36
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△π
Lv.9
2020.07.11 16:44
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