Congruence Transf

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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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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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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

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