Geometry & Measures
Grade 1-3Properties of 2D Shapes
Examiners regularly test whether you can name a shape from a short list of properties, or list the properties of a shape from its name, so this is a topic where precise vocabulary matters as much as understanding. This lesson covers naming triangles by their side and angle properties, naming quadrilaterals from their sides and angles, naming polygons by their number of sides, and finding lines of symmetry and order of rotational symmetry.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Types of triangle
An equilateral triangle has three equal sides and three equal angles of 60°. An isosceles triangle has exactly two equal sides and two equal angles. A scalene triangle has three sides of different lengths and three different angles. A right-angled triangle has one angle of exactly 90°.
A triangle with sides of 4 cm, 6 cm and 8 cm, all different, is scalene. A triangle with one angle marked 90° is right-angled, regardless of its side lengths.
Types of quadrilateral
A square has four equal sides and four right angles. A rectangle has two pairs of equal, parallel sides and four right angles, but its sides are not all equal. A rhombus has four equal sides and two pairs of parallel sides, but no right angles. A parallelogram has two pairs of equal, parallel sides and equal opposite angles, with no right angles. A trapezium has exactly one pair of parallel sides. A kite has two pairs of adjacent sides equal, and one line of symmetry along its axis.
The key distinction between a rhombus and a square is that both have four equal sides, but only a square has four right angles, a rhombus does not need right angles at all.
Naming polygons
A polygon is named according to its number of sides: a pentagon has 5 sides, a hexagon has 6, a heptagon has 7, an octagon has 8, and a decagon has 10. A regular polygon has all sides and all angles equal; an irregular polygon does not.
A polygon with 5 sides of different lengths and 5 different angles is irregular, since not all of its sides and angles are equal, even though it still has 5 sides and could be called a pentagon.
Symmetry
A line of symmetry is a line that divides a shape into two mirror-image halves. The order of rotational symmetry is the number of times a shape looks exactly the same during one full 360° turn.
A regular hexagon has 6 lines of symmetry and rotational symmetry of order 6, since it has 6 identical sides. A rectangle that is not a square has only 2 lines of symmetry, since only the two lines through the midpoints of opposite sides create mirror images.
Worked Examples
Three exam-style questions, fully solved.
A quadrilateral has four equal sides and four right angles. What is the name of this quadrilateral?
Easy- 1.Match the properties to the correct quadrilateral: four equal sides and four right angles is the defining property of a square
Answer: Square
A quadrilateral has four equal sides, but its diagonals are not equal in length. What is the name of this quadrilateral?
Medium- 1.Four equal sides suggests either a square or a rhombus
- 2.A square would have equal diagonals, so unequal diagonals rules out a square
Answer: Rhombus
A student says, "every rhombus is a square." Is the student correct? Explain your answer.
Hard- 1.Compare the defining properties of each shape: both have four equal sides
- 2.A square must also have four right angles, but a rhombus does not need right angles
Answer: No, the student is not correct, since a rhombus has four equal sides but its angles are not necessarily 90°, while a square must have four right angles
Avoid These
The most common mistakes students make.
Confusing a rhombus with a square, forgetting that a rhombus does not need right angles even though both shapes have four equal sides.
Confusing a rectangle with a parallelogram, forgetting that a rectangle specifically needs four right angles.
Naming a polygon by guessing rather than counting its sides carefully, especially mixing up heptagon (7 sides) and octagon (8 sides).
Giving the order of rotational symmetry instead of the number of lines of symmetry, or the other way round, when a question asks for one specific measure.
Assuming a shape with 5 sides is automatically regular, when a polygon is only regular if all of its sides and all of its angles are equal.
FAQ
Questions parents and students ask.
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