Properties of 2D Shapes
Properties of 2D shapes is about naming and using the properties of triangles (equilateral, isosceles, scalene and right-angled), quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium and kite), and regular versus irregular polygons. Properties include how many sides are equal in length, which sides are parallel, which angles are equal or right angles, and how the diagonals behave (whether they are equal, bisect each other, or cross at right angles).
Before you start
Make sure you're comfortable with these topics first:
Method
- Count the number of sides to identify the general shape family, for example a quadrilateral has 4 sides and a pentagon has 5 sides.
- Check the side lengths: are any sides equal, and are any sides parallel? This narrows down which quadrilateral or triangle it must be.
- Check the angles: are any right angles present, and are opposite angles equal?
- If diagonals are shown, check whether they bisect each other, whether they are equal in length, and whether they cross at right angles.
- Use the shape's known properties, such as 'a rhombus has all four sides equal and opposite sides parallel', to find missing side lengths or angles.
- For a regular polygon, remember that all sides are the same length and all interior angles are the same size.
Worked example
A quadrilateral has all four sides equal in length, and its diagonals cross at right angles but are not equal in length. Name the quadrilateral, and state one further property of its angles.
- All four sides equal narrows the shape down to a square or a rhombus.
- A square has diagonals that are equal in length, but this shape's diagonals are not equal, so it cannot be a square.
- A rhombus has all sides equal and diagonals that cross at right angles but are not equal in length, which matches every property given.
- The quadrilateral is a rhombus.
- A further property: opposite angles of a rhombus are equal, and the diagonals bisect the angles at each vertex.
Practice questions
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Q1Name a quadrilateral with two pairs of parallel sides, all four sides equal, but no right angles.Show answer
Answer: Rhombus
Q2Name a triangle with all three sides of different lengths.Show answer
Answer: Scalene triangle
Q3How many lines of symmetry does a square have?Show answer
Answer: 4
Q4Name the quadrilateral with exactly one pair of parallel sides.Show answer
Answer: Trapezium
Q5State two properties of a parallelogram.Show answer
Answer: Opposite sides are equal and parallel, and opposite angles are equal.
Q6A kite has how many pairs of adjacent equal sides?Show answer
Answer: 2 pairs (two separate pairs of adjacent sides are equal)
Q7Name a triangle with one angle of 90 degrees and no equal sides.Show answer
Answer: Right-angled scalene triangle
Q8Is every square also a rectangle? Explain your answer.Show answer
Answer: Yes, because a square has four right angles and opposite sides that are equal and parallel, which satisfies the definition of a rectangle.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A quadrilateral ABCD has AB parallel to DC, AB = DC, and all four angles equal to 90 degrees, but AB is longer than BC. Name the quadrilateral, and give a reason for your answer.
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Triangle XYZ is isosceles with XY = XZ. Angle XYZ = 68 degrees. (a) Work out angle XZY. (b) Work out angle YXZ. (c) State whether the triangle is acute-angled, right-angled or obtuse-angled.
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Free printable worksheet
Want more practice on paper? Download the properties of 2d shapes worksheet pack - 6 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 5 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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