Question

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

part a
is △abc a right triangle? explain your reasoning.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the longest side.

Step2: Substitute side lengths of $\triangle ABC$

$AB=12$, $BC=5$, $AC=13$. Calculate $12^2 + 5^2$:
$12^2 + 5^2 = 144 + 25 = 169$

Step3: Compare to longest side squared

$AC^2 = 13^2 = 169$
Since $12^2 + 5^2 = 13^2$, the triangle satisfies the theorem.

Answer:

Yes, $\triangle ABC$ is a right triangle. It satisfies the Pythagorean theorem: $12^2 + 5^2 = 13^2$, so $\angle B$ is the right angle.