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

/ 18

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
Two co-interior angles of a parallelogram are (3x + 10)° and (x + 30)°. Determine the value of x, and hence the size of each angle.
(4)
Co-interior angles of a parallelogram add up to 180° (1)
4x + 40 = 180 (1)
x = 35 (1)
The angles are 115° and 65° (1)✓✓✓✓ (4)
2
Define a parallelogram.
(2)
A quadrilateral with both pairs of opposite sides parallel.✓✓ (2)
3
Which quadrilateral has diagonals that are equal AND bisect each other?
(1)
A rectangle (and therefore also a square).✓ (1)
4
Which quadrilateral has perpendicular diagonals that bisect the angles?
(1)
A rhombus (and therefore also a square).✓ (1)
5
How many pairs of parallel sides does a trapezium have?
(1)
One✓ (1)
6
Do a kite's diagonals bisect each other?
(1)
No — only one diagonal bisects the other, and it does so perpendicularly.✓ (1)
7
In parallelogram ABCD, Â = 70°. Find Ĉ and B̂.
(2)
Ĉ = 70° (opposite angles equal); B̂ = 110° (co-interior)✓✓ (2)
8
State five ways to prove a quadrilateral is a parallelogram.
(4)
Opposite sides parallel; opposite sides equal; opposite angles equal; diagonals bisect each other; one pair opposite sides equal and parallel.✓✓✓✓ (4)
9
Is every rectangle a parallelogram? Is every parallelogram a rectangle?
(2)
Yes to the first; no to the second.✓✓ (2)

TOTAL: 18 marks