Question

PLEASE HELP!!!! PLEASE..

13. Each pair of polygons is similar. Write a similarity statement for the polygons. Then, find the measure of x, the measures of the indicated sides, and the scale factor.

Answer 1

Option A:

ΔDEF
`\sim` ΔABC; x = 1.5; CB = 3.9; AB = 3;
`(2)/(3)`

Solution:

Each pair of given polygons are similar.

Similarity statement for the given polygons:

In ΔDEF and ΔABC,

∠D = ∠A (Angle)

∠E = ∠B (Angle)

Therefore, ΔDEF
`\sim` ΔABC (by AA similarity)

If two triangles are similar, then their sides are proportional.

`$\Rightarrow (DF)/(AC) =(DE)/(AB)`

`$\Rightarrow (2.4)/(3.6) =(2)/(2x)`

Do cross multiplication,

⇒ 2.4 × 2x = 2 × 3.6

⇒ 4.8x = 7.2

⇒ x = 1.5

Substitute x = 1.5 in CB and AB,

CB = 3x – 0.6

= 3(1.5) – 0.6

CB = 3.9

AB = 2x

= 2(1.5)

AB = 3

Scale factor means ratio of the sides of the triangle.

`$\Rightarrow (DF)/(AC) =(2.4)/(3.6)=(2)/(3)`

Therefore, Option A is the correct answer.

Hence ΔDEF
`\sim` ΔABC; x = 1.5; CB = 3.9; AB = 3;
`(2)/(3)`.