Junior Secondary · Mathematics

Quadrilateral: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Quadrilateral.

10 questions24 marksFree, no account

Question 1

1 mark

Which of the following properties is ALWAYS true for a rhombus but NOT necessarily true for a general parallelogram?

Question 2

1 mark

In a parallelogram $ABCD$, $\angle B = (5x + 10)^\circ$ and $\angle D = (3x + 40)^\circ$. Find the value of $x$.

Question 3

1 mark

In a rectangle $$PQRS$$, the diagonals $$PR$$ and $$QS$$ intersect at $$O$$. If $$\angle POQ = 120^\circ$$, find the measure of $$\angle OPS$$.

Question 4

1 mark

In a parallelogram $PQRS$, the lengths of opposite sides are given as $PQ = (2x + 5)$ cm and $SR = (x + 12)$ cm. Find the value of $x$.

Question 5

1 mark

In a quadrilateral $ABCD$, it is given that $AB = CD$ and $AB \parallel CD$. If $\angle A = 2x + 10^\circ$ and $\angle B = 3x - 5^\circ$, find the value of $x$.

Question 6

2 marks

In a parallelogram ABCD, if the length of side BC is 15 cm and the length of side CD is 8 cm, find the length of side AD.

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

In an isosceles trapezoid ABCD, the side AD is parallel to the base BC. If the measure of the angle $\angle DAB$ is $115^\circ$, find the measures of the angles $\angle ABC$ and $\angle BCD$.

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Question 8

4 marks

Given a parallelogram $$ABCD$$, where $$E$$ and $$F$$ are the midpoints of sides $$AB$$ and $$CD$$ respectively. Prove that the quadrilateral $$AECF$$ is a parallelogram.

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Question 9

5 marks

A rhombus PQRS has its diagonals PR and QS intersecting at point O. Given that $ \angle QPR = 40^\circ $.

a) State the relationship between adjacent angles in a rhombus.

b) Find the measure of $ \angle QPS $.

c) Find the measures of $ \angle PRS $ and $ \angle PQR $.

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

In a rectangle ABCD, AD = 6 cm and AB = 8 cm. The diagonal AC is drawn. Point E is on AC such that DE is perpendicular to AC.

a) Find the length of the diagonal AC.

b) Find the area of triangle ADC.

c) Using your answers from (a) and (b), find the length of DE.

Write your answer out first, then check it against the worked solution.

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