For a triangle ABC, prove that angle C is a right angle if and only if the median of side c is c/2

Kyle Liu

Kyle Liu

Answered question

2022-07-25

For a triangle ABC, prove that angle C is a right angle if and only if the median of side c is c/2

Answer & Explanation

Jaylynn Huffman

Jaylynn Huffman

Beginner2022-07-26Added 14 answers

use Thales's theorem
any right triangle will circumcise a half circle. and therefore its center O coincise the angular bisector , and the hypotheseus is its diameter, and the median from the right angle of the triangle, is its radius, thus = 1/2 diamter. and it's always true.
Thale's theorem proof:
We use the following facts:
the sum of the angles in a triangle is equal to two right angles (180

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