Question

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

Explanation:

Step1: Use the property of reflection

When a figure is reflected across a line, the corresponding segments are congruent. So, \(AB = A'B\) and \(AC=A'C\).

Step2: Analyze the side - lengths of \(\triangle ACA'\)

Since reflection across \(BC\) maps \(A\) to \(A'\), we know that \(BC\) is the perpendicular bisector of \(AA'\). Let's consider the lengths. By the definition of reflection, \(AC = A'C\). In \(\triangle ACA'\), two sides (\(AC\) and \(A'C\)) are congruent.

Answer:

\(\triangle ACA'\) is an isosceles triangle. Because when we reflect \(\triangle ABC\) across \(BC\) to get \(\triangle A'BC\), \(AC = A'C\) (reflection preserves side - lengths), and a triangle with two congruent sides is an isosceles triangle.