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Primary 5 Parallelogram, Rhombus and Trapezium study guide: the whole chapter, step by step
About this subtopic
This mixed practice stop brings together 3 topics from Primary 5 Parallelogram, Rhombus and Trapezium: Three four-sided figures, Four-sided figures, Drawing on a grid. Nothing on the question says which topic it comes from, so choosing the method is part of the skill.
Practice questions with worked solutions
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Start the 7-day free trialQuestion 1 of 3 · Intermediate · free to tryThe figure shows quadrilateral JKLM with triangle MLN joined to it along ML…The figure shows quadrilateral…
The figure shows quadrilateral JKLM with triangle MLN joined to it along ML. KLN is a straight line. JK = 8 cm, LN = 8 cm and angle LNM = 64°. The figure is not drawn to scale. Find angle MJK.
Show the working and the answer
Working
- JK and ML each carry one arrowhead and KL and JM each carry two, so both pairs of opposite sides of JKLM are parallel and JKLM is a parallelogram
- opposite sides of a parallelogram are equal in length, so ML = JK = 8 cm
- LN is 8 cm as well, so triangle MLN has two sides of the same length and is isosceles
- ∠LMN = ∠LNM = 64° (base angles of triangle MLN, whose sides ML and LN are both 8 cm)
- ∠MLN = 180° − 64° − 64° = 52° (angle sum of triangle MLN)
- ∠KLM = 180° − 52° = 128° (angles on the straight line KLN)
- ∠MJK = ∠KLM = 128° (opposite angles of parallelogram JKLM)
Answer: 128°
For parents
How do you approach P5 parallelogram, rhombus and trapezium mixed practice?
These questions draw a line across a four-sided figure, or join a triangle to it, and ask for an angle or for the name of a new shape.
What your child learns here
These questions draw a line across a four-sided figure, or join a triangle to it, and ask for an angle or for the name of a new shape. Your child uses the properties of the parallelogram, rhombus and trapezium to find angles, then uses the angles to decide which sides are parallel. Both directions belong to the Primary 5 outcomes on the properties of these shapes and on finding unknown angles without drawing extra lines.
- A parallelogram has two pairs of parallel sides, and its opposite angles are equal.
- A rhombus is a parallelogram with four equal sides.
- A trapezium has one pair of parallel sides and no second pair.
- Between two parallel sides, the two angles on the same side add up to 180°.
- To name a shape, check each pair of sides for parallel lines using the angles between them.
Does the answer make sense?
In the parallelogram PQRS, angle QPT is 180° minus 72°, which is 108°, and angle PTU is 180° minus 116°, which is 64°. These two add to 172°, not 180°, so TU is not parallel to PQ. PT and QU are parallel because they lie on the parallelogram's sides, so PQUT has exactly one pair and is a trapezium.
How to practise these questions
All three questions are Intermediate. One draws a line across a parallelogram and asks your child to name the four-sided piece it cuts off, which means finding its angles and checking which sides are parallel. One draws a line from a corner of a four-sided figure and asks for the angle it makes with a parallel side. One joins a triangle to a four-sided figure along a straight line, with two equal sides, so an angle is carried from the triangle into the figure. Ask your child to mark the parallel sides with arrows before starting.
Questions parents ask
Is a rhombus also a parallelogram? Yes. A rhombus has two pairs of parallel sides, like every parallelogram, and in addition all four of its sides are equal.
How can angles show that two sides are parallel? If the two angles between a pair of sides, on the same side of a line crossing them, add up to 180°, the sides are parallel. If they do not, the sides are not parallel.
Are the diagonal properties of these shapes taught in Primary 5? The Primary 5 syllabus lists no diagonal property. When a line is drawn across one of these shapes, your child works with the triangles and smaller four-sided shapes it makes.