Question

Which reason can be used to fill in the numbered blank space?

1) 1. ��abc ��bed
2. side-angle-side similarity postulate
2) 1. ��abc ��bed
2. side-side-side similarity theorem
3) 1. ��abc ��dbe
2. side-angle-side similarity postulate
4) 1. ��abc ��dbe
2. side-side-side similarity theorem

Answer 1

Option 3 is the correct answer as it correctly pairs the corresponding vertices of the two triangles and cites the Side-Angle-Side similarity postulate, which requires two sides to be proportional and the included angles to be equal in both triangles for them to be similar.

Step-by-step explanation:

The question is asking which statement correctly explains a possible similarity between the given triangles ►c and ▾d. We have four options, each describing a pair of triangles and the reason for their similarity. For triangles to be similar, there must be a correspondence between their angles and sides that satisfy certain conditions based on geometric postulates or theorems. The Side-Angle-Side (SAS) Similarity Postulate indicates that two triangles are similar if two sides are proportional and the included angle is equal in both triangles. The Side-Side-Side (SSS) Similarity Theorem states that two triangles are similar if all three sides of one triangle are proportional to the corresponding sides of the other triangle.

Now, reviewing the options we see that option 3 is the correct one:

1. ►c ≅ ▽be
2. Side-Angle-Side similarity postulate

This is correct because it has both the right correspondence of triangle vertices and the correct postulate that can be used to determine the similarity between the two triangles. Thus, option 3) ►c ≅ ▽be with Side-Angle-Side similarity postulate is the correct answer.