Question

1. reasoning

in the sign, ∠1 ≅ ∠2 and ∠2 ≅ ∠3. classify the triangle and justify your answer.

Explanation:

Step1: Use transitive property of congruence

Since $\angle1\cong\angle2$ and $\angle2\cong\angle3$, then $\angle1\cong\angle3$ by the transitive property of congruence.

Step2: Recall triangle - classification rules

A triangle with all angles congruent is an equiangular triangle. In an equiangular triangle, all sides are also congruent, so it is also an equilateral triangle.

Answer:

The triangle is an equilateral (and equiangular) triangle because $\angle1\cong\angle2\cong\angle3$ which implies all angles of the triangle are congruent.