Question

two triangles share a 90° angle and a 45° angle. what can be said about the triangles? a. they are congruent. b. they are proportional but not similar. c. they are similar by the aa criterion. d. they are not similar. what does it mean if the sides of two triangles are proportional? a. the triangles have equal perimeters. b. the triangles are equal in area. c. the triangles are congruent. d. the triangles are similar.

Explanation:

If the sides of two triangles are proportional, by the definition of similar - triangles, the triangles are similar. The AA (angle - angle) criterion is for showing similarity based on equal angles, not related to the side - proportionality condition here. Proportional sides do not imply congruence (congruent triangles have equal sides), equal area, or equal perimeters. For two triangles with angles 90° and 45°, the third angle in each triangle is 45° (since the sum of angles in a triangle is 180°). By the AA criterion, they are similar.

Answer:

For the first question: d. The triangles are similar.
For the second question: c. They are similar by the AA criterion.