Question

use the pythagorean theorem to determine if the triangle is a right triangle. try another one. heres a new triangle. is this triangle a right triangle? remember, it might not be drawn to scale. use the pythagorean theorem to check. you can solve on paper and then enter your answer on zearn. if the sides of a triangle, a, b, and c, make the equation $a^2 + b^2 = c^2$ true, then the triangle is a right triangle and the longest side, c, is the hypotenuse. the triangle dropdown a right triangle. the sum of the squares of the shorter sides, $a^2 + b^2$, dropdown the square of the longest side, $c^2$. the triangle has sides 7, 6, 9 (with 9 as the hypotenuse candidate).

Explanation:

Step1: Identify sides

Let \(a = 6\), \(b = 7\), \(c = 9\) (longest side).

Step2: Calculate \(a^2 + b^2\)

\(a^2 + b^2 = 6^2 + 7^2 = 36 + 49 = 85\)

Step3: Calculate \(c^2\)

\(c^2 = 9^2 = 81\)

Step4: Compare

\(85
eq 81\), so \(a^2 + b^2
eq c^2\). Thus, the triangle is not a right triangle, and \(a^2 + b^2\) is not equal to \(c^2\).

Answer:

The triangle is not a right triangle. The sum of the squares of the shorter sides, \(a^2 + b^2\), is not equal to the square of the longest side, \(c^2\).