Which quadrilateral has exactly one pair of parallel sides?
A) Parallelogram
B) Trapezium
C) Kite
D) Square
E) Rhombus
(Total for Question 1 is 1 mark)
2
Which quadrilateral has all four sides equal but does not have to have all angles equal?
A) Rectangle
B) Parallelogram
C) Rhombus
D) Kite
E) Trapezium
(Total for Question 2 is 1 mark)
3
Which quadrilateral has diagonals that bisect each other and are equal in length, but are not perpendicular?
A) Square
B) Rhombus
C) Rectangle
D) Kite
E) Parallelogram
(Total for Question 3 is 1 mark)
4
Which quadrilateral always has four lines of symmetry?
A) Rectangle
B) Parallelogram
C) Square
D) Kite
E) Rhombus
(Total for Question 4 is 1 mark)
5
What is the order of rotational symmetry of a square?
A) 1
B) 2
C) 3
D) 4
E) 8
(Total for Question 5 is 1 mark)
6
In parallelogram ABCD, angle A is 65 degrees. Work out the sizes of angles B, C and D.
(Total for Question 6 is 3 marks)
7
State the order of rotational symmetry of a rectangle that is not a square.
A) 1
B) 2
C) 3
D) 4
E) 8
(Total for Question 7 is 1 mark)
8
A convex quadrilateral has three angles of 95 degrees, 85 degrees and 100 degrees. Work out the size of the fourth angle.
(Total for Question 8 is 2 marks)
9
A rhombus has one interior angle of 120 degrees. Find the sizes of all four interior angles.
(Total for Question 9 is 3 marks)
10
A rectangle is not a square.
(a)How many lines of symmetry does it have?(1)
(b)What is its order of rotational symmetry?(1)
(Total for Question 10 is 2 marks)
11
Does every parallelogram have a line of symmetry? Give a reason for your answer.
(Total for Question 11 is 2 marks)
12
Name the quadrilateral that has two pairs of adjacent equal sides (each pair next to each other) but whose opposite sides are not equal.
(Total for Question 12 is 1 mark)
13
A pupil writes: "The interior angles of a quadrilateral add up to 180 degrees." Is the pupil correct? Explain briefly.
(Total for Question 13 is 2 marks)
14
An isosceles trapezium (ABCD with AB parallel to CD and AD = BC) is drawn.
(a)How many lines of symmetry does this isosceles trapezium have?(1)
(b)What is its order of rotational symmetry?(1)
(Total for Question 14 is 2 marks)
15
A quadrilateral has four lines of symmetry. What must its order of rotational symmetry be?
(Total for Question 15 is 1 mark)
16
A kite has diagonals of lengths 10 cm and 24 cm which meet at right angles. Calculate the area of the kite.
(Total for Question 16 is 2 marks)
17
Explain what is meant by 'order of rotational symmetry 2' for a shape.
(Total for Question 17 is 1 mark)
18
Which quadrilateral always has all interior angles equal?
A) Parallelogram
B) Rhombus
C) Kite
D) Rectangle
E) Trapezium
(Total for Question 18 is 1 mark)
19
Which property is true for every parallelogram?
A) Diagonals are perpendicular
B) Opposite sides are equal and parallel
C) Has four lines of symmetry
D) All angles are 90 degrees
E) All sides are equal
(Total for Question 19 is 1 mark)
20
A quadrilateral has all four sides equal and its diagonals are equal in length. Name this quadrilateral.
(Total for Question 20 is 1 mark)
Mark scheme · EP.M118 Properties of Quadrilaterals and Symmetry
Question 1
B1 correct option B (Trapezium) cao
Answer: B) Trapezium (one pair of parallel sides). The other options have either two pairs or none of the single-pair property; a parallelogram, square and rhombus have two pairs, a kite has no parallel pairs in general.)
Question 2
B1 correct option C (Rhombus) cao
Answer: C) Rhombus
Question 3
B1 correct option C (Rectangle) cao
Answer: C) Rectangle (its diagonals bisect each other, are equal in length and, unless it is a square, are not perpendicular).
Question 4
B1 correct option C (Square) cao
Answer: C) Square
Question 5
B1 correct option D (4) cao
Answer: D) 4
Question 6
M1 Use that opposite angles in a parallelogram are equal; deduce angle C = 65
M1 Use that adjacent angles are supplementary; deduce angle B = 180 - 65 = 115
A1 All three angles correct: B = 115, C = 65, D = 115 cao
Answer: Angle B = 115 degrees, angle C = 65 degrees, angle D = 115 degrees
Question 7
B1 correct option B (2) cao
Answer: B) 2
Question 8
M1 Add the three given angles to find their total: 95 + 85 + 100 = 280
A1 360 - 280 = 80, fourth angle 80 degrees cao
Answer: 80 degrees
Question 9
M1 Use that opposite angles in a rhombus are equal; deduce the opposite angle = 120
M1 Use that adjacent angles are supplementary; calculate adjacent angle = 180 - 120 = 60
A1 All angles correct: 120, 60, 120, 60 cao
Answer: 120, 60, 120, 60 degrees
Question 10
(a) B1 2 lines of symmetry cao
(a) Answer: 2
(b) B1 Order 2 cao
(b) Answer: 2
Question 11
B1 No (simple correct statement) cao
A1 Reason: opposite sides are parallel but angles need not be equal; only special parallelograms (rectangles, rhombuses) have symmetry ao
Answer: No. A general parallelogram need not have equal adjacent angles or equal adjacent sides, so it does not necessarily have a line of symmetry; only special cases like rectangles or rhombuses do.
Question 12
B1 Kite cao
Answer: Kite
Question 13
B1 State that the pupil is incorrect cao
A1 Give correct reason: sum is 360 degrees since (4 - 2) x 180 = 360 or split into two triangles ao
Answer: No. A quadrilateral's interior angles sum to 360 degrees because (4 - 2) x 180 = 360, or by dividing the quadrilateral into two triangles each with sum 180.
Question 14
(a) B1 1 line of symmetry cao
(a) Answer: 1
(b) B1 Order 1 cao
(b) Answer: 1
Question 15
B1 Order 4 cao
Answer: 4
Question 16
M1 Use area formula for kite/orthogonal diagonals: (1/2) x d1 x d2
A1 Area = (1/2) x 10 x 24 = 120 cm2 cao
Answer: 120 cm2
Question 17
B1 Correct explanation: the shape matches itself after rotation by 180 degrees (and 360 degrees) cao
Answer: It means the shape maps onto itself after a rotation of 180 degrees (and again at 360 degrees).
Question 18
B1 correct option D (Rectangle) cao
Answer: D) Rectangle
Question 19
B1 correct option B (Opposite sides are equal and parallel) cao