Question

A triangle has sides a , b , and c . Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed if a=3 , b=4 , and c=5 .

Answer 1

[AI-generated answer — Bot GPT 3.5]

The Converse of the Pythagorean Theorem states that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Using this, we can determine if a right triangle can be formed with sides a = 3, b = 4, and c = 5 by checking if the equation a^2 + b^2 = c^2 holds true.

In this case, 3^2 + 4^2 = 9 + 16 = 25, which is equal to 5^2.

Since a^2 + b^2 = c^2 is true, a right triangle can be formed using these side lengths.