Question

which of the following pairs show(s) triangles that are similar but not congruent? b only b and c only a and c only a, b, and c

Explanation:

Step1: Recall the criteria for similar and congruent triangles

Similar triangles have equal - corresponding angles and proportional - corresponding sides. Congruent triangles have equal - corresponding angles and equal - corresponding sides (a special case of similar triangles where the ratio of similarity is \(1\)).

Step2: Analyze pair A

For pair A, assume the triangles. If two angles of one triangle are equal to two angles of another triangle (by AA - Angle - Angle similarity criterion), the triangles are similar. But if the sides are not equal (by visual inspection of the side - lengths from the figure, they seem to have different side - lengths), they are not congruent.

Step3: Analyze pair B

For pair B, using the AA criterion (right - angle and one other equal angle), the triangles are similar. And since the side - lengths (by visual inspection of the figure) are not equal, they are not congruent.

Step4: Analyze pair C

For pair C, using the AA criterion (two equal angles), the triangles are similar. And by visual inspection of the side - lengths from the figure, they are not equal, so they are not congruent.

Answer:

A, B, and C