 Middle Years

7.02 Transformations and congruence

Worksheet
Rigid transformations
1

State whether the following pairs of triangles are a translation, rotation or reflection of one another:

a
b
c
2

For each of the following, describe the translation from figure A to figure B:

a
b
c
d
e
f
g
h
3

Determine whether the following diagrams show a reflection across the given line:

a
b
c
d
e
4

Consider the following shape:

Draw the shape after it has been rotated by 180 \degree clockwise about point A.

5

For each of the following:

i

Find the clockwise angle of rotation of shape A to shape B about point O.

ii

Find the anticlockwise angle of rotation of shape A to shape B about point O.

a
b
6

Consider the figures shown:

a

What type of transformation can take triangle A to triangle B?

b

Identify the transformation from triangle A to triangle B.

7

Consider the figures shown:

a

b

8

Consider the figures shown:

a

What type of transformation can transform triangle A to triangle B?

b

Identify the transformation from triangle A to triangle B.

9

Consider the figures shown.

What are the possible types of transformations that could get rectangle A to rectangle B?

Congruence
10

The given diagram shows 2 triangles that are translations of one another:

State the angle that has the same size as \angle CBA.

11

The given diagram shows 2 triangles that are rotations of one another:

State the angle that has the same size as \angle PRQ.

12

The given diagram shows 2 triangles that are reflections of one another:

State the angle that has the same size as \angle RPQ.

13

The given diagram shows 2 triangles that are translations and reflections of one another:

State the angle that has the same size as \angle CBA.

14

\triangle ABC is reflected along the dotted line and its image XYZ is produced.

a

Find the length of each side:

i

XY

ii

YZ

iii

XZ

b

Describe the relationship between \triangle XYZ and \triangle ABC.

15

\triangle ABC is translated to the right to form \triangle DEF:

a

State which side of \triangle DEF corresponds to BC.

b

State which angle of \triangle DEF corresponds to \angle BCA.

c

If AC = 14\text{ cm}, find the length of DF.

d

If the smallest angle in \triangle DEF is \angle EFD, state the smallest angle in \triangle ABC.

16

Given that the following shapes are congruent, find the value of x.

17

Given that the following triangles are congruent, find the values of x and y.

18

Given that \triangle BAC \equiv \triangle FED, which angle of \triangle FED corresponds to \angle ABC?

19

Which side is equal to AB in \triangle DFE?

Bisectors
20

State whether the following triangles have a line of symmetry:

a
b
c
d
e
f
21

Consider \triangle PQR with midpoint X at side PR:

a

State what type of triangle is \triangle PQR.

b

State whether the following is correct.

i

\angle QXR \gt \angle QXP

ii

\angle QXR = \angle QXP

iii

\angle QXR \lt \angle QXP

c

Is the line through Q and X a line of symmetry for \triangle PQR?

d

Are \angle RQX and \angle PQX equal or not equal?

22

Consider \triangle PQR with angle bisector PX of \angle QPR and QR=12:

a

State what type of triangle is \triangle PQR.

b

State whether the following is correct.

i

Q X \gt R X

ii

Q X = R X

iii

Q X \lt R X

c

Is the line through P and X a line of symmetry for \triangle PQR?

d

Are \angle PXR and \angle PXQ equal or not equal?

23

Consider the \triangle PQR with midpoint Xat side PR:

a

State what type of triangle is \triangle PQR.

b

Determine whether the following is correct.

i

\angle QXR \gt \angle QXP

ii

\angle QXR = \angle QXP

iii

\angle QXR \lt \angle QXP

c

Is the line through Q and X a line of symmetry for \triangle PQR?

d

Are \angle RQX and \angle PQX equal or not equal?

24

Consider \triangle PQR with angle bisector QX at \angle PQR:

a

State what type of triangle is \triangle PQR.

b

Determine whether the following is correct.

i

P X \gt R X

ii

P X = R X

iii

P X \lt R X

c

Is the line through Q and X a line of symmetry for \triangle PQR?

d

Are \angle QXR and \angle QXP equal or not equal?