Chapter 2: Geometry

Test C (40 marks)

Part A – Multiple-choice (10 marks)

1 The value of x in the following diagram is:

A 72 B 126 C 68

D 54 E 108

2 The size of an interior angle of a regular pentagon is:

A 90° B 60° C 135°

D 108° E 120°

Questions 3 and 4 refer to the pair of triangles below.

3 The value of x above is:

A 3 B 6 C 9

D 19.2 E 369
4 The scale factor of the pair of similar triangles above is:

A B C

D E 3

5 If = 76°, is:

A 76° B 140° C 104°

D 208° E 52°

6 is:

A 154° B 103° C 77°

D 90° E 206°
7 In the following diagram, if APY = 63° and BPX = 57°, then ABP is:

A 63° B 114° C 57°

D 60° E 126°

8 The value of a in the triangle shown is:

A 52 B 102 C 128

D 258 E 256

9 A cube has side length 5 cm. A second cube has a volume of 8000 cm 3. The area of
the face of the second cube is:

A 4 faces bigger than a face of the first cube

B 16 times bigger than a face of the first cube

C 64 times bigger than a face of the first cube

D the same as a face of the first cube

E 4 times smaller than a face of the first cube

A 225 B 270 C 120

D 180 E 240
Part B – Short-answer (21 marks)

1 Find the value of x in each of the following, giving reasons.

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(1 + 1 = 2 marks)

2 For this question consider the diagram shown

a Prove ∆AOB  ∆POQ.

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b Hence explain why AO = OP.

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 c If AP is 12cm in length, what is the length of side OP?

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((2  ½) + 1 = 2 marks)

3 The two shapes below are similar.

a Find the value of x.

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b Find the value of y.

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(1 + 1 = 2 marks)

4 Use the circle theorems to find the value of the pronumeral(s) in these circles.

a b

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 c d

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(½ + 1 + ½ + 1 = 3 marks)

5 Find the value of x in each figure.

a b

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(3  1 = 3 marks)
6 Find the value of the pronumerals in the following diagrams.

a b

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c d

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(2 + 2 + 2 + 3 = 9 marks)
Part C – Extended-response (9 marks)

1 Consider the following diagram of parallelogram ABCD.

a Prove ∆ABC  ∆DCB.

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b Hence, prove that opposite sides of a parallelogram are parallel.

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Now consider the following diagram of quadrilateral EFGH.

c Prove ∆EFG  ∆HGF.

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(3 × 2 = 6 marks)
2 Chris can see a tree on the opposite bank of a river. He decides to place rocks
(indicated with dots) on his side of the river to try to calculate the river's width.
He measures the distances between some pairs of rocks and finds that BC = 44 m,
CD = 8.8 m and DE = 12.25 m, as shown in the diagram below.

Find the width of the river.

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(3 marks)