Geometry: Properties of Shapes and Angles (Year 6)
Geometry: Properties of Shapes and Angles (Year 6) covers identifying and describing 2D and 3D shapes by their properties, calculating missing angles using known angle facts, and naming and comparing different types of triangle and quadrilateral.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the key angle facts first: angles on a straight line sum to 180 degrees, angles around a point sum to 360 degrees, angles in a triangle sum to 180 degrees, and angles in a quadrilateral sum to 360 degrees.
- To find a missing angle, add up all the angles you already know, then subtract this total from the correct sum for that shape or arrangement.
- Learn to name triangles by their properties: equilateral (three equal sides and angles), isosceles (two equal sides and angles), scalene (no equal sides or angles), and right-angled (one 90 degree angle).
- Learn to name quadrilaterals by their properties: a square has four equal sides and four right angles, a rectangle has two pairs of equal sides and four right angles, a rhombus has four equal sides but no right angles, and a parallelogram has two pairs of parallel sides.
- Use a protractor to measure or draw angles accurately, lining up the base line of the protractor exactly with one arm of the angle.
- When comparing two shapes, check every property in turn - number of sides, side lengths, angle sizes, and whether any sides are parallel - rather than relying on how the shape looks at first glance.
Worked example
A triangle has one angle of 90 degrees and another angle of 35 degrees. Work out the size of the third angle, then state what type of triangle it is.
- Use the fact that angles in a triangle sum to 180 degrees.
- Add the two known angles together: 90 + 35 = 125 degrees.
- Subtract this total from 180 to find the missing angle: 180 - 125 = 55 degrees.
- Since one angle is exactly 90 degrees, and all three angles (90, 35 and 55 degrees) are different sizes, the triangle is a right-angled scalene triangle.
Practice questions
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Q1Two angles lie on a straight line. One is 47 degrees. What is the other?Show answer
Answer: 133 degrees
Q2Three angles meet at a point. Two of them are 110 degrees and 130 degrees. What is the third?Show answer
Answer: 120 degrees
Q3A triangle has angles of 60 degrees, 60 degrees and 60 degrees. What type of triangle is this?Show answer
Answer: An equilateral triangle
Q4A quadrilateral has angles of 90, 90 and 60 degrees. What is the fourth angle?Show answer
Answer: 120 degrees (360 - 90 - 90 - 60)
Q5Name a quadrilateral with four equal sides but no right angles.Show answer
Answer: A rhombus
Q6A triangle has two equal angles of 50 degrees each. What is the third angle?Show answer
Answer: 80 degrees (180 - 50 - 50)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A triangle has angles of 42 degrees and 79 degrees. Work out the third angle.
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Four angles meet at a point. Three of them are 85 degrees, 95 degrees and 100 degrees. Work out the fourth angle.
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Mia says that a rectangle and a rhombus are really the same shape, just turned around, because they both have four sides. Explain why Mia is wrong.
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Free printable worksheet
Want more practice on paper? Download the geometry: properties of shapes and angles (year 6) 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.
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