명제의 증명과 절대부등식 연습문제 — Sundstrom, Mathematical Reasoning · 3.2절 · 8c번

Sundstrom, Mathematical Reasoning · 3.2절 · 8c번영어 원문

For a right triangle, suppose that the hypotenuse has length $c$ feet and the lengths of the sides are $a$ feet and $b$ feet.

Prove that the right triangle described above is an isosceles triangle if and only if the area of the right triangle is $\dfrac{1}{4} c^2$ .

정답·풀이 보기 (영어 원문)

Prove both of the conditional statements: (1) If the area of the right triangle is $c^2/4$ , then the right triangle is an isosceles triangle. (2) If the right triangle is an isosceles triange, then the area of the right triangle is $c^2/4$ .

한 번 더 — 비슷한 문제Sundstrom, Mathematical Reasoning · 3.2절 · 3b번영어 원문

Complete the following.

Is this statement true or false? Prove the statement if it is true or provide a counterexample if it is false.

다 풀었으면 정답 확인

The statement is true. If $a = b$ , then $\dfrac{a + b}{2} = \dfrac{2a}{2} = a$ , and $\sqrt{ab} = \sqrt{a^2} = a$ . This proves the contrapositive.

이 문제로 이어서 풀기

# 명제의 증명과 절대부등식증명·논술자동 분류