Question

Determine whether the polygons to the right are similar. If​ so, write a similarity statement and give the scale factor. If​ not, explain.

Answer 1

E, Yes. ∆HJK ~ ∆STV. The scale factor is ½.

Explanation:

1. Similarity statement

When you name similar triangles, the order of the letters of corresponding angles must be in matching order.

For example, in ∆HJK, ∠H is the right angle, ∠J is the larger acute angle, and ∠K is the smallest angle.

The corresponding parts in ∆STV are ∠S, ∠T, and ∠V.

The similarity statement is

∆HJK ~ ∆STV

2. Scale factor

The scale factor (C) is the ratio of corresponding parts of the two triangles.

If ∆HJK is transformed to ∆STV, the scale factor is

`C = \frac{\text{ST}}{\text{HJ}} = \frac{\text{TV}}{\text{JK}} = \frac{\text{SV}}{\text{HK}}\\\\C = (5)/(10) = (13)/(26) = (12)/(24) = \mathbf{(1)/(2)}\\\\\text{The scale factor is $\large \boxed{\mathbf{(1)/(2)}}$}`