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 △ABC side lengths

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

Step3: Calculate square of longest side

$AC^2 = 13^2 = 169$

Step4: Compare the two results

$12^2 + 5^2 = 13^2$, so the theorem holds.

Answer:

Yes, $\triangle ABC$ is a right triangle. The side lengths satisfy the Pythagorean theorem: $12^2 + 5^2 = 13^2$ ($144 + 25 = 169$), confirming it is a right triangle (right-angled at $B$).