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

Answer:

(a) Similar polygons; scale factor is 2

(b) Similar polygons; scale factor is 1.5

Step-by-step explanation:

Given

See attachment for polygons

Required

Determine if they are similar or not

Solving (a): The triangle

The angles in both triangles show that the triangles are similar

To calculate the scale factor (k), we simply take corresponding sides.

i.e.

$k = \frac{DF}{BA} = \frac{FE}{AC} = \frac{DE}{BC}$

$k = \frac{6}{3} = \frac{8}{4} = \frac{10}{5}$

$k = 2=2=2$

$k = 2$

The scale factor is 2

Solving (b): The trapezium

The angles in both trapeziums show that the trapeziums are similar

To calculate the scale factor (k), we simply take corresponding sides.

i.e.

$k = \frac{KN}{GJ}$

$k = \frac{6}{4}$

$k = 1.5$

The scale factor is 1.5