Question

pythagorean theorem converse hw1.2b
#8. is the triangle shown a right triangle? how do you know?
14 feet
13 feet
24 feet
because
yes
no

Explanation:

Step1: Recall Pythagorean theorem converse

The converse of the Pythagorean theorem states that if \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side of a triangle and \(a\) and \(b\) are the other two sides, then the triangle is a right - triangle.

Step2: Identify the sides

Let \(a = 13\), \(b = 14\), and \(c = 24\) (since \(24\) is the longest side).

Step3: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

Calculate \(a^{2}+b^{2}\): \(13^{2}+14^{2}=169 + 196=365\). Calculate \(c^{2}\): \(24^{2}=576\).

Step4: Compare

Since \(13^{2}+14^{2}=365
eq576 = 24^{2}\), the triangle is not a right - triangle.

Answer:

No