Question

which triangles are congruent to △a? choose all that apply. triangle d triangle e which triangles are similar to △a? choose all that apply. triangle b triangle c triangle d triangle e

Explanation:

Step1: Recall congruence criteria

Two triangles are congruent if they have the same shape and size. We can check side - lengths and angles by counting grid units.

Step2: Analyze triangle A and others for congruence

By counting the grid - based side - lengths of the triangles, we find that triangle D has the same side - lengths as triangle A. Triangle E has different side - lengths. So the congruent triangle to A is triangle D.

Step3: Recall similarity criteria

Two triangles are similar if their corresponding angles are equal and the ratios of their corresponding side - lengths are equal.

Step4: Analyze triangle A and others for similarity

Triangle B has a different shape. Triangle C has the same shape as triangle A (right - angled and the ratio of the sides is the same). Triangle D has the same shape as triangle A (congruent triangles are also similar). Triangle E has a different shape. So the similar triangles to A are triangle C and triangle D.

Answer:

1. A. Triangle D
2. C. Triangle C, D. Triangle D