This test consists of four sections with marks allocated as indicated below:

Section A Vocabulary 5 marksSeciton B Multiple Choice 10 marksSection C Short Answer 20 marksSection D Analysis 5 marksTOTAL 40 marks

Section A: Vocabulary

Place the correct word from the list below in the appropriate space:

1. Shapes are ___________________ when they are identical in every

respect.

2. Similar shapes have the same ________________ but differ in

____________.

3. The number by which the sides of a shape are multiplied to produce

another similar shape is called the __________________ .

4. If the value of the number in Question 3 is more than 1, then the original

shape is _________________ .

WORD LIST

common factor multiple shrunk

scale factor shape enlarged

size sidelengths congruent

Parade College Mathematics Department 2014 Chapter 10 Test: Deductive Geometry

Name: _________________________

Section B: Multiple Choice

Question 1

Which of the following triangles would be congruent to ABC?

A B

C D

E

Question 2

Question 3

The values of c and d, respectively, in the pair of congruent triangles in the figure below are:

A 15 and 55°B 7.5 and 25°C 15 and 70°D 15 and 110°E 7.5 and 55°

The value of a in the pair of similar triangles below is:

A 2

B 3

C

D

E

Question 4

The test you could use to prove that TRS SUT is:

A SASB AASC RHSD AAAE SSS

Question 5

The value of a in the pair of similar triangles in the figure below is:

A

BC 28

D

E

Question 6

Consider the diagram below:

What congruency law could be used to prove that ∆ DEA ≅∆ ECB ?

A. AAAB. RHSC. SSSD. ASAE. The two triangles are not congruent.

Question 7

Which of the following properties is not true for a rhombus?

A Opposite angles are equal.B Diagonals are perpendicular.C All four sides are equal.D Diagonals bisect the angles of a rhombus.E Only one pair of opposite sides are parallel.

Question 8

Which of the following statements is not true?

A A square is a trapezium.B A rhombus is a parallelogram.C A square is a rectangle.D The diagonals of a parallelogram bisect each other. E A rectangle is a parallelogram.

Question 9

Which of the following properties is true for a rectangle?

A Diagonals bisect the angles they pass through.B All sides are equal.C Diagonals are perpendicular.D Diagonals are equal.E Opposite angles sum to 90°.

Question 10

Which of the following properties are not true about a parallelogram?

A Opposite sides are parallel.B Opposite sides are equal.C Diagonals are equal.D Opposite angles are equal.E Angles sum to 360°.

Section C: Short Answer Questions

In this section, relevant working must be shown to gain full marks.

Question 1

Consider the diagram shown below:

16

6

9

Find the value of b. Make sure that you show all steps clearly.

3 marks

Question 2

Find the values of p and q in the diagram below:

4 marks

Question 3

Are the following two triangles similar? Explain your answer.

2 marks

Question 4

2 marks

Find the values of d and e in the following pair of congruent triangles.

Question 5

Consider the two triangles shown in the diagram below:

Show that these two triangles are similar by using the appropriate Similarity test. Make sure that you clearly state what test you are using.

3 marks

Question 6

a. Name a quadrilateral that has exactly one pair of parallel sides.

b. Name a quadrilateral that has all sides equal, but whose interior angles are not all equal.

c. Name a quadrilateral whose diagonals bisect each other, but are not at right angles to each other.

3 marks

Question 7

Consider the diagram below:

The points A, B, D and E lie on a circle. The point C is the centre of the circle. Prove that the triangles ABE and BDE are congruent. Make sure that you clearly state the Congruency test that you use.

3 marks

Section D: Analysis Section

Question 1

Consider the diagram below:

a. Explain why AGBis equal to DGC .

1 mark

b. Prove that ∆ AGB is congruent to ∆ DGC . Clearly state the Congruency test that you use.

2 marks

c. Prove that ∆ ACBis congruent to ∆ DBC .

2 marks