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

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Grade 10 · Euclidean Geometry

Properties of Quadrilaterals & Their Proofs (Grade 10)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Define a parallelogram.
(2)
A quadrilateral with both pairs of opposite sides parallel.✓✓ (2)
2
Which quadrilateral has diagonals that are equal AND bisect each other?
(2)
A rectangle (and therefore also a square).✓✓ (2)
3
Which quadrilateral has perpendicular diagonals that bisect the angles?
(2)
A rhombus (and therefore also a square).✓✓ (2)
4
How many pairs of parallel sides does a trapezium have?
(2)
One✓✓ (2)
5
Do a kite's diagonals bisect each other?
(2)
No — only one diagonal bisects the other, and it does so perpendicularly.✓✓ (2)
6
In parallelogram ABCD, ∠A = 70°. Find ∠C and ∠B.
(2)
∠C = 70° (opposite angles equal); ∠B = 110° (co-interior)✓✓ (2)
7
State five ways to prove a quadrilateral is a parallelogram.
(2)
Opposite sides parallel; opposite sides equal; opposite angles equal; diagonals bisect each other; one pair opposite sides equal and parallel.✓✓ (2)
8
Is every rectangle a parallelogram? Is every parallelogram a rectangle?
(2)
Yes to the first; no to the second.✓✓ (2)

TOTAL: 16 marks