Question

Which triangle is similar to triangle AEB using the pieces of right triangles similarity theorem? a) Triangle DCE b) Triangle ECB c) Triangle BEC d) Triangle CED

Answer 1

Triangle ECB is similar to triangle AEB using the pieces of right triangles similarity theorem.

Step-by-step explanation:

The triangle that is similar to triangle AEB using the pieces of right triangles similarity theorem is triangle ECB.

According to the right triangle similarity theorem, if two triangles have a shared angle between their corresponding sides, then they are similar.

In triangle ECB, angle E is shared with triangle AEB, and the corresponding sides EB and EC are proportional to EA and EB, respectively, which satisfies the similarity condition.

Answer 2

Based on the image you sent and the Pieces of Right Triangles Similarity Theorem, the triangle similar to triangle AEB is c) Triangle BEC.

Here's why:

Pieces of Right Triangles Similarity Theorem:

This theorem states that if a line is drawn parallel to one side of a right triangle, intersecting the other two sides, the resulting smaller triangle is similar to the original triangle.

Analyzing the Triangles:

In the image, we see:

Triangle AEB is a right triangle with AE as the hypotenuse and AB and BE as the legs.

Line DC is parallel to AB.

Triangle BEC is formed by the intersection of DC with legs AB and BE.

According to the theorem, Triangle BEC should be similar to Triangle AEB because DC is parallel to AB. They will have corresponding angles that are congruent and corresponding sides that are proportional.

Checking other options:

Triangle DCE shares a leg (CE) with Triangle AEB, but it is not formed by a line parallel to another side. Hence, it is not similar.

Triangle ECB shares a leg (EB) with Triangle AEB, but it is not formed by a line parallel to another side. Hence, it is not similar.

Triangle CED shares no sides or angles with Triangle AEB. Therefore, it is not similar.

Conclusion:

Therefore, based on the Pieces of Right Triangles Similarity Theorem and the properties of the triangles in the image, Triangle BEC is the only triangle similar to Triangle AEB.

Complete the image: