New Zealand
Level 6 - NCEA Level 1

# Transformations and Similarity

Lesson

In Changing Shapes, we looked at how congruent shapes may be transformed in one or more ways on a number plane. We can also transform similar shapes. These similar shapes will be dilated by a scale factor (ie. enlarged or reduced by a certain ratio) in addition to the transformation. The video attached to the examples below explains this process.

#### Examples

##### Question 1

Consider the figures shown.

1. Are the two triangles congruent, similar or neither?

Congruent

A

Similar

B

Neither

C

Congruent

A

Similar

B

Neither

C
2. What is the transformation from triangle $ABC$ABC to triangle $A'B'C'$ABC?

Dilation

A

Reflection

B

Rotation

C

Translation

D

Dilation

A

Reflection

B

Rotation

C

Translation

D
3. What is the scale factor of the dilation from triangle $ABC$ABC to triangle $A'B'C'$ABC?

##### Question 2

Consider the quadrilateral with vertices at $A$A$\left(-3,-3\right)$(3,3), $B$B$\left(-3,3\right)$(3,3), $C$C$\left(3,3\right)$(3,3) and $D$D$\left(3,-3\right)$(3,3), and the quadrilateral with vertices at $A'$A$\left(-9,-9\right)$(9,9), $B'$B$\left(-9,9\right)$(9,9), $C'$C$\left(9,9\right)$(9,9) and $D'$D$\left(9,-9\right)$(9,9).

1. Are the two rectangles similar, congruent or neither?

congruent

A

similar

B

neither

C

congruent

A

similar

B

neither

C
2. What is the transformation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$ABCD?

dilation

A

reflection

B

rotation

C

translation

D

dilation

A

reflection

B

rotation

C

translation

D
3. What is the scale factor of the dilation of rectangle $ABCD$ABCD to rectangle $A'B'C'D'$ABCD?

##### Question 3

The quadrilateral with vertices at $\left(9,9\right)$(9,9), $\left(0,9\right)$(0,9), $\left(0,0\right)$(0,0) and $\left(9,0\right)$(9,0) is rotated 90 degrees clockwise around the origin and dilated by a factor of 2 with the origin as the centre of dilation.

What are the new coordinates of the vertices of the quadrilateral?

1. Write all four coordinates on the same line, separated by commas.

### Outcomes

#### GM6-5

Recognise when shapes are similar and use proportional reasoning to find an unknown length

#### GM6-8

Compare and apply single and multiple transformations

#### 91031

Apply geometric reasoning in solving problems

#### 91034

Apply transformation geometry in solving problems