Question

jacqueline constructed triangle abc, where m∠a = 53°, and m∠b = 112°. ruthie constructed triangle rst, where m∠s = 112°, and m∠t = 15°. are the two triangles similar? explain your reasoning.

Explanation:

Step1: Find angle C in triangle ABC

The sum of angles in a triangle is 180°. So, $m\angle C=180^{\circ}-(m\angle A + m\angle B)$. Substituting $m\angle A = 53^{\circ}$ and $m\angle B=112^{\circ}$, we get $m\angle C=180-(53 + 112)=180 - 165=15^{\circ}$.

Step2: Check for angle - angle similarity

In triangle ABC, angles are $53^{\circ},112^{\circ},15^{\circ}$. In triangle RST, angles are $112^{\circ},15^{\circ}$ (given). Since two pairs of corresponding angles are equal ($m\angle B=m\angle S = 112^{\circ}$ and $m\angle C=m\angle T = 15^{\circ}$), by the AA (angle - angle) similarity criterion, the two triangles are similar.

Answer:

Yes, the two triangles are similar because two pairs of corresponding angles are equal.