Question

question 2
use triangles abc and rst to answer the following questions.

part a
is \\( \triangle abc \\) a right triangle? explain your reasoning.

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). In \(\triangle ABC\), let \(a = 5\), \(b=12\), and \(c = 13\).

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

• Calculate \(a^{2}+b^{2}\): \(5^{2}+12^{2}=25 + 144=169\)
• Calculate \(c^{2}\): \(13^{2}=169\)

Since \(5^{2}+12^{2}=13^{2}\), by the converse of the Pythagorean theorem, \(\triangle ABC\) is a right - triangle.

Answer:

Yes, \(\triangle ABC\) is a right - triangle. Because \(5^{2}+12^{2}=25 + 144 = 169\) and \(13^{2}=169\), so \(5^{2}+12^{2}=13^{2}\), which satisfies the Pythagorean theorem.