Question

1. given: ∠dce ≅ ∠b

prove: △abc is an isosceles triangle.

Explanation:

Step1: Use vertical angles

$\angle DCE\cong\angle ACB$ (vertical angles are congruent)

Step2: Substitute using given

Since $\angle DCE\cong\angle B$ (given), then $\angle ACB\cong\angle B$ (substitution)

Step3: Use triangle property

In $\triangle ABC$, if $\angle ACB=\angle B$, then $AC = AB$ (if two angles of a triangle are congruent, then the sides opposite those angles are congruent)

Answer:

Since $AC = AB$, $\triangle ABC$ is an isosceles triangle.