Question

Question: Consider the similarity transformation of ΔABC to produce ΔEDF.

1. Create a sequence of transformations of ΔABC to produce ΔEDF.

2. Justify your transformation of ΔABC to produce ΔEDF in terms of similarity.

Answer 1

Answer:

see the explanation

Step-by-step explanation:

we have triangle  ΔABC

step 1

Rotate 90 degrees clockwise ΔABC about point C to obtain ΔA'B'C'

Remember that

A rotation is a rigid transformation

An object and its rotation are the same shape and size, but the figures may be turned in different directions

so

ΔABC and ΔA'B'C' are congruent

ΔABC≅ ΔA'B'C

step 2

Dilate the triangle ΔA'B'C' to obtain triangle ΔEDF

Remember that

A dilation is a non rigid transformation

A dilation produces similar figures

If two figures are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent

Find the scale factor of the dilation

The scale factor is equal to the ratio of corresponding sides

In this problem

Let

z ----> the scale factor

so

$z=\frac{ED}{AB}=\frac{DF}{BC}=\frac{EF}{AC}$

Multiply the length sides of triangle ΔA'B'C' by the scale factor z to obtain the length sides of triangle ΔEDF

Note: in this problem the scale factor z is less than 1

That means ----> the dilation is a reduction