Question

1. reflect right triangle abc across line bc. classify triangle aca according to its side lengths. explain how you know.

Explanation:

Step1: Recall reflection property

A reflection is a rigid - motion. Rigid motions preserve side - lengths and angle - measures. So, when right - triangle $ABC$ is reflected across line $BC$ to form triangle $ACA'$, we know that $AB = A'B$ and $AC=A'C$.

Step2: Analyze side - length classification

In triangle $ACA'$, since $AC = A'C$, two sides of the triangle are equal. A triangle with two equal sides is an isosceles triangle.

Answer:

Triangle $ACA'$ is an isosceles triangle. This is because a reflection is a rigid motion that preserves side - lengths, and after reflecting right - triangle $ABC$ across line $BC$, we have $AC = A'C$, which is the definition of an isosceles triangle.