Properties of Quadrilaterals and Symmetry
Quadrilaterals are 2D shapes with four straight sides. 11+ papers test naming and identifying quadrilaterals from their properties, such as square, rectangle, parallelogram, rhombus, trapezium and kite, along with their side, angle and diagonal properties, plus both line symmetry (folding a shape so both halves match) and rotational symmetry (turning a shape so it looks the same as its start).
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn to name each quadrilateral: square, rectangle, parallelogram, rhombus, trapezium and kite, and know which of them have parallel sides.
- Learn the side-length and angle properties of each shape, for example, a rhombus has four equal sides but does not need right angles, while a parallelogram has two pairs of equal, parallel sides and equal opposite angles.
- Remember that the angles inside any quadrilateral always sum to 360 degrees, which is useful for finding a missing angle.
- To find lines of symmetry, imagine folding the shape in half along different lines and check whether both halves match exactly.
- To find the order of rotational symmetry, imagine turning the shape a full 360 degrees and count how many times it looks exactly the same as it did at the start.
- When asked to identify a shape from a list of clues, work through each type of quadrilateral in turn and eliminate any that fail to fit every clue.
Worked example
A quadrilateral has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. It is not a parallelogram. Name this quadrilateral, and state its number of lines of symmetry.
- Exactly one pair of parallel sides identifies the shape as a trapezium, since a parallelogram, rectangle, square and rhombus all have two pairs of parallel sides.
- The extra clue that the two non-parallel sides are equal in length tells us it is specifically an isosceles trapezium, rather than a general trapezium.
- An isosceles trapezium has one line of symmetry, running vertically through the midpoints of the two parallel sides.
- So the shape is an isosceles trapezium, with 1 line of symmetry.
Practice questions
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Q1Name a quadrilateral with four equal sides and four right angles.Show answer
Answer: Square
Q2Name a quadrilateral with two pairs of parallel sides and equal opposite angles, but sides that are not all equal and no right angles.Show answer
Answer: Parallelogram
Q3How many lines of symmetry does a rectangle that is not a square have?Show answer
Answer: 2
Q4What is the order of rotational symmetry of a square?Show answer
Answer: 4
Q5A quadrilateral has angles of 130, 130, 50 and x degrees. Find x.Show answer
Answer: 50 (360 - (130+130+50) = 360 - 310)
Q6Name a quadrilateral that has exactly one pair of parallel sides.Show answer
Answer: Trapezium
Q7Does a rhombus always have four right angles? Explain your answer.Show answer
Answer: No. A rhombus has four equal sides, but its angles are only right angles in the special case where it is also a square; otherwise its opposite angles are equal but not 90 degrees.
Q8What is the order of rotational symmetry of a rectangle that is not a square?Show answer
Answer: 2
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A quadrilateral has exactly two pairs of adjacent equal sides (so two sides meeting at one vertex are equal, and the other two sides meeting at the opposite vertex are equal, but the two pairs are different lengths), and one pair of opposite angles are equal. Name the quadrilateral and state its number of lines of symmetry.
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In a quadrilateral, the angles are 3x, 2x, 4x and x degrees. (a) Form and solve an equation to find x. (b) Find the size of the largest angle. (c) The quadrilateral has one pair of parallel sides and no line of symmetry. What type of quadrilateral could it be?
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Free printable worksheet
Want more practice on paper? Download the properties of quadrilaterals and symmetry worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 33 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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