# 4.05 Transformations, congruence, and similarity

## Interactive practice questions

Consider the figures shown.

a

Are the two quadrilaterals similar, congruent or neither?

Congruent

A

Similar

B

Neither

C

Congruent

A

Similar

B

Neither

C
b

What single transformation could have been used from quadrilateral $ABCD$ABCD to quadrilateral $A'B'C'D'$ABCD?

Dilation

A

Reflection

B

Rotation

C

Translation

D

Dilation

A

Reflection

B

Rotation

C

Translation

D
c

Identify the transformation from quadrilateral $ABCD$ABCD to quadrilateral $A'B'C'D'$ABCD.

A reflection across the line $y=5$y=5.

A

A reflection across the $y$y-axis.

B

A reflection across the $x$x-axis.

C

A reflection across the line $y=5$y=5.

A

A reflection across the $y$y-axis.

B

A reflection across the $x$x-axis.

C
Easy
Less than a minute

Consider the figures shown.

Consider the figures shown.

Consider the figures shown.

### Outcomes

#### GEO-G.CO.2

Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.

#### GEO-G.CO.3

Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that map the polygon onto itself.

#### GEO-G.CO.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

#### GEO-G.SRT.1

Verify experimentally the properties of dilations given by a center and a scale factor.

#### GEO-G.SRT.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.