Question

Jose constructed Triangle DCE, where m∠D = 103° and m∠C = 22°. Remy constructed triangle PQT, where m∠Q = 22°, and m∠T = 55°. Are the two triangles similar to one another? *

Yes, because two pairs of corresponding angles in the triangles are congruent.



No, because none of the corresponding pairs of angles in the triangles are congruent.



No, because 103 + 22 ≠ 22 + 55.



There is not enough information to determine if the two triangles are similar to one another.

Answer 1

Yes

Explanation:

They are similar by angle-angle similarly theorem

In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar . (Note that if two pairs of corresponding angles are congruent, then it can be shown that all three pairs of corresponding angles are congruent, by the Angle Sum Theorem.)

Answer 2

The missing angle in Jose's triangle is 180 - 103 - 22 = 55° and since both triangles have two congruent pairs of corresponding angles the answer is yes.