Question

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

1) 1. Δabc Δbed
2. side-angle-side similarity postulate
2) 1. Δabc Δbed
2. side-side-side similarity theorem
3) 1. Δabc Δdbe
2. side-angle-side similarity postulate
4) 1. Δabc Δdbe
2. side-side-side similarity theorem

Answer 1

The correct reason that can be used to fill in the numbered blank space is option 2: 1. Δabc Δbed 2. side-angle-side similarity postulate.

Step-by-step explanation:

The correct reason that can be used to fill in the numbered blank space is option 2: 1. Δabc Δbed 2. side-angle-side similarity postulate.

The side-angle-side (SAS) similarity postulate states that if two sides of one triangle are proportional to two sides of another triangle, and the included angle in both triangles is congruent, then the triangles are similar.

In this case, Δabc and Δbed have a side AB proportional to side BE, side BC proportional to side ED, and the included angle ∠ABC congruent to ∠BED, satisfying the conditions of the SAS similarity postulate. Therefore, Δabc and Δbed are similar triangles.