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수학동아 - 폴리매스
함께 풀고 싶은 문제
나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.
[문장제 문제&개념응용] [(오랜만에)기하] 사각형의 증명
17수락
2020.12.07 20:41
조회 354
*단순문제/성의없는문제로 여겨질 시 말씀해주세요
수락은 여러 사각형이 어떤 조건에서 성립하는지 궁금해서 직접 증명을 하려고 한다
그럼 문제 나갑니다
사각형 ABCD에 대해
1) 사각형 ABCD가 평행사변형이고 AC와 BD의 길이가 같으면 직사각형이 된다는것을 증명하여라
2) 사각형 ABCD가 평행사변형이고 AC와 BD가 수직으로 만나면 마름모가 된다는것을 증명하여라
3) 등변사다리꼴에서 밑변의 양 끝 각이 같다고 가정하였을때
(1) 사다리꼴 안에 이등변삼각형을 이용하여 두 변의 길이가 같다는것을 증명하여라
(2) 사다리꼴 안에 수선의 발을 이용하여 두 변의 길이가 같다는것을 증명하여라
(3) 사다리꼴의 연장선을 이용하여 두 변의 길이가 같다는것을 증명하여라
4) (약간 단순문제) 사각형의 순서도에서(사각형->사다리꼴->평행사변형......) 각 사각형이 다음 사각형이 되기 위한 조건을 모두 서술하시오.(단,마름모와 직사각형의 관계도 증명하시오)
5) 외접사각형에서 AD+BC=AB+CD인것과 사각형의 넓이를 구하는 공식을 서술하고 증명하시오
7) 내접사각형에서 내대각과 핟각(이였나?) 의 크기가 같다는것을 증명하시오
지금 바로
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