Properties of Quadrilaterals & Their Proofs (Grade 10) — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 10 · Euclidean Geometry

Properties of Quadrilaterals & Their Proofs (Grade 10)

EXAM-STYLE CLASS TEST

Marks

Duration

45 minutes

Questions

Name:

Class:

Date:

Mark

/ 30

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
Which property does a RECTANGLE have that a general parallelogram does NOT?
(1)
A)its diagonals are equal
B)its opposite sides are parallel
C)its diagonals bisect each other
D)its opposite angles are equal
1.2
Which property does a RHOMBUS have that a rectangle does NOT?
(1)
A)its diagonals cross at right angles
B)its diagonals are equal
C)its opposite angles are equal
D)its opposite sides are parallel
1.3
A quadrilateral with exactly ONE pair of parallel sides is a …
(1)
A)trapezium
B)parallelogram
C)kite
D)rhombus
1.4
In parallelogram ABCD, ∠A = 70°. Then ∠B = …
(1)
A)110°
B)70°
C)20°
D)290°
1.5
Which ONE of these proves that a quadrilateral is a parallelogram?
(1)
A)both pairs of opposite sides are equal
B)one pair of opposite sides is equal
C)the diagonals are equal
D)one pair of opposite angles is equal
1.6
The diagonals of a KITE …
(1)
A)cross at 90°, and the long one bisects the other
B)bisect each other
C)are equal
D)are both axes of symmetry
1.7
The interior angles of any quadrilateral add up to …
(1)
A)360°
B)180°
C)540°
D)720°
1.8
In rhombus PQRS the diagonals meet at T. Then △PTQ is …
(1)
A)right-angled
B)equilateral
C)obtuse-angled
D)scalene with no special angle
1.9
A square is …
(1)
A)both a rectangle and a rhombus
B)a rectangle but not a rhombus
C)a rhombus but not a rectangle
D)neither a rectangle nor a rhombus
1.10
In parallelogram ABCD, AB = 3x − 4 and DC = x + 8. Then x = …
(1)
A)6
B)3
C)4
D)12

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[9 MARKS]

ABCD is a parallelogram. It is given that Â = (3x + 10)° and Ĉ = (5x − 30)°.

2.1
Give a reason why Â = Ĉ.
(2)
2.2
Calculate the value of x.
(3)
2.3
Hence calculate the size of Â and of B̂, with reasons.
(4)

Question 3

[11 MARKS]

Answer the questions below on the properties of quadrilaterals.

3.1
State THREE properties that a rhombus has but a general parallelogram does not.
(3)
3.2
A quadrilateral has one pair of opposite sides both parallel AND equal. Prove that it must be a parallelogram.
(3)
3.3
A quadrilateral has diagonals that bisect each other at right angles but are NOT equal in length. Name the quadrilateral and give a reason.
(3)
3.4
Explain why every square is a rectangle, but not every rectangle is a square.
(2)

TOTAL: 30 marks

This question paper consists of 3 questions.

Statement	Reason

Statement	Reason

Statement	Reason

Statement	Reason