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

(a) Similar polygons; scale factor is 2

(b) Similar polygons; scale factor is 1.5

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 = (DF)/(BA) = (FE)/(AC) = (DE)/(BC)`

`k = (6)/(3) = (8)/(4) = (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 = (KN)/(GJ)`

`k = (6)/(4)`

`k = 1.5`

The scale factor is 1.5