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Mathematics for Australia Year 8 - Homework CONGRUENCE AND TRANSFORMATIONS (Chapter 17)
Under a translation, every point on the figure moves a
fixed distance in a given direction.
1 Translate the given
figure 5 units left and
2 units down.
2 Determine the
translation from A to
A0 in the following:
3 a Translate ABCD 6 units right and 4 units up.
b State the vertex coordinates of the image.
4 Reflect the following figure in the mirror line given:
5 a Reflect ABC in the:
i x-axis ii y-axis.
b For each reflection in a, state the vertex coordinates
of the image.
i
ii
A rotation is a transformation in which every point on
the figure is turned through a given angle about a fixed
point.
The fixed point is called the centre of rotation and is
usually labelled O.
6 Rotate the given
figure about O
through 180.
7
a State the vertex coordinates of ABCD.
b Rotate the figure 270 clockwise about O.
c State the vertex coordinates of the image.
TRANSFORMATIONS17A
CHAPTER 17: CONGRUENCE AND TRANSFORMATIONS
REMINDER
REMINDER
A
A0
m
y
x
5
-5
-5 5
A
C
B
O
y
x
5
-5
-55
CD
BA
y
x
5
-5
-5 5
A D
B C
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CONGRUENCE AND TRANSFORMATIONS (Chapter 17) Mathematics for Australia Year 8 - Homework
Two figures arecongruent if one figure lies exactly on top
of the other after a combination of translations, rotations,and reflections.
1 Are the following pairs of figures congruent?
a
b
2 Which two of these figures are congruent?
A B
C D
3 Quadrilaterals PQRS and WXYZ are congruent.
Determine the:
a length of [QR] b size of QbPS
c perimeter of PQRS.
4 Show that A is congruent to B by transforming A to Bin a single transformation.
5 Show that A is congruent to B by transforming A to B
in a combination of transformations.
6 Are the following pairs of figures congruent?
a
b
CONGRUENT FIGURES17B
REMINDER
y
x
5
-5
-55
B
A
y
x
5
-5
-55
A
B
y
x
5
-5
-55
y
x
5
-5
-55
Y
X
W
Z
26 cm
58 cm
40 cm
58 cm
56105
109
P Q
R
S
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Mathematics for Australia Year 8 - Homework CONGRUENCE AND TRANSFORMATIONS (Chapter 17)
Two triangles are congruent if any one of the following
is true: All corresponding sides are equal in length. (SSS)
Two sides and theincluded angleare equal. (SAS)
Two angles and a pair ofcorresponding sides areequal. (AAcorS)
For right angled triangles, the hypotenuses and onepair of sides are equal. (RHS)
1 State whether these pairs of triangles are congruent,giving reasons for your answers:
a
b
c
d
e
f
2 Which of the following
triangles is congruent to
the one alongside?
A B
C D
3 The following pairs of triangles are not drawn to scale.
Determine whether each pair is congruent. If it is, what
else can we deduce about them?
a
b
c
CONGRUENT TRIANGLES17C
REMINDER
60
70
5060
70
50
4545
30
35 30
35
112 23
5 cm
45
23
5 cm
23112
5 cm
11245
23
5 cm
112
23
A B
C
E
F
D
S
R
T30
60
W
X Y30
GH
F
J
K
L
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CONGRUENCE AND TRANSFORMATIONS (Chapter 17) Mathematics for Australia Year 8 - Homework
d
1 Consider the isosceles
triangle shown alongside.
a Complete the following:
In triangles ABM and ACM:
AB = ............... fgiveng
A bMB = ............... = ..........
f......................................................g
[AM] is ......................... to both triangles.
) 4ABM=4ACM f.......................................g
Equating corresponding angles, B bAM = ...............
b What property of isosceles triangles has been proven
in a?
2 Consider the rectangle
PQRS.
a Show that 4PQR=4SRQ.
b Explain why PR= SQ.
c What property of rectangles has been proven?
3 The diagonals of parallelogram EFGH meet at P, as
shown.
a Show that 4EPF=4GPH.
b Explain why EP = GP.
c Explain why HP = FP.
d What property of parallelogram has been proven in
c and d?
PROOF USING CONGRUENCE17D
5 cm
11 cm
A C
B
80
80
5 cmQ R
P
11 cm
B CM
A
P Q
S R
E
H
P
F
G
4 Use congruence to show that
the opposite angles of a
rhombus are equal in size.
A B
CD
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Mathematics for Australia Year 8 - Homework CONGRUENCE AND TRANSFORMATIONS (Chapter 17)
REVIEW OF CHAPTER 17
1 Translate the given figures in the direction indicated.
a
5 units down
b
1 unit left and
4 units up
2 State the translation that maps A onto B.
3 a Reflect ABCD in the x-axis.
b State the coordinates of the image vertices.
4 Rotate A 90 anticlockwise about O.
5 Show that A is congruent to B by transforming A to B
in a series of transformations:
6 The following pairs of triangles are not drawn to scale.
Determine whether each pair is congruent. If it is, what
else can we deduce about them?
a
b
7 Use congruence to show that the diagonals of a rectangle
bisect each other.
y
x
5
-5
-55
y
x
5
-5
-55
B
A
y
x
5
-5
-55
A
D
C
B
y
x
5
-5
-55
A
A
B
B C
A
D E
F
R
QP
66 44
6670
X
W Y
11104
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