 # 4.05 Transformations, congruence, and similarity

## Interactive practice questions

Consider the figures shown.

a

Which term best describes the relationship between the two triangles ?

Congruent

A

Similar

B

Neither

C
b

What single transformation can take triangle $ABC$ABC to triangle $A'B'C'$ABC?

Reflection

A

Rotation

B

Translation

C

Dilation

D
c

Identify the transformation from triangle $ABC$ABC to triangle $A'B'C'$ABC.

A translation $2$2 units left and $3$3 units down.

A

A translation $3$3 units left and $2$2 units down.

B

A translation $2$2 units right and $3$3 units up.

C

A translation $3$3 units right and $2$2 units up.

D
Easy
Approx a minute

Consider the figures shown.

Consider the triangle with vertices at $\text{A(-4, -1), B(1, 3) and C(2, -3)}$A(-4, -1), B(1, 3) and C(2, -3), and the triangle with vertices at $\text{A'(0, -3), B'(5, 1) and C'(6, -5)}$A'(0, -3), B'(5, 1) and C'(6, -5).

$\Delta(FGH)$Δ(FGH) and $\Delta(F''G''H'')$Δ(FGH) are shown on the coordinate plane below.

### 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.