New Zealand
Level 6 - NCEA Level 1

# Transformations and Similarity

## Interactive practice questions

Consider the figures shown.

a

Are the two triangles congruent, similar or neither?

Congruent

A

Similar

B

Neither

C

Congruent

A

Similar

B

Neither

C
b

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
c

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

Easy
Approx a minute

Consider the figures shown.

Consider the triangle with vertices at $A$A$\left(-3,-2\right)$(3,2), $B$B$\left(2,1\right)$(2,1) and $C$C$\left(3,-3\right)$(3,3), and the triangle with vertices at $A'$A$\left(-9,-6\right)$(9,6), $B'$B$\left(6,3\right)$(6,3) and $C'$C$\left(9,-9\right)$(9,9).

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).

### 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