Question

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

Explanation:

Step1: Property of reflection

When a figure is reflected across a line, the corresponding segments are congruent. So, \(AC = A'C\) (by the property of reflection).

Step2: Definition of isosceles triangle

A triangle with at least two congruent sides is an isosceles triangle. In \(\triangle ACA'\), since \(AC = A'C\), it satisfies the condition of an isosceles triangle.

Answer:

\(\triangle ACA'\) is an isosceles triangle. Because when right - triangle \(ABC\) is reflected across line \(BC\), \(AC\) and \(A'C\) are congruent (by the property of reflection), and a triangle with two congruent sides is an isosceles triangle.