Question

3 - 9 practice online
geometry (s1 p01 rm h218) sharp, jeffrey / unit 3 - similarity / lesson 3 - 9 conditions for triangle similarity

1. refer to the figure.

complete the explanation to determine whether triangles abc and dec are similar.
by the _ theorem, there are 2 pairs of congruent corresponding angles, so they are similar by the _ triangle similarity theorem.

Explanation:

Step1: Identify vertical angles

Vertical angles are congruent. In the figure, \(\angle ACB\) and \(\angle DCE\) are vertical angles. So \(\angle ACB\cong\angle DCE\).

Step2: Identify another pair of congruent angles

Given \(\angle A = 36^{\circ}\) and \(\angle D=36^{\circ}\), so \(\angle A\cong\angle D\).

Step3: Apply triangle similarity theorem

By the Vertical Angles Theorem, \(\angle ACB\cong\angle DCE\). We have two pairs of congruent angles (\(\angle A\cong\angle D\) and \(\angle ACB\cong\angle DCE\)). By the AA (Angle - Angle) Triangle Similarity Theorem, if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Answer:

By the Vertical Angles Theorem, there are 2 pairs of congruent corresponding angles, so they are similar by the AA Triangle Similarity Theorem.