Primary 5 · Measurement & Geometry
P5 parallelogram, rhombus and trapezium
A parallelogram, a rhombus and a trapezium are four-sided shapes told apart by their parallel and equal sides. In P5, your child learns the properties of quadrilaterals like these, and uses them to find unknown angles.
- Taught in
- Term 4
- Syllabus
- 2 skills
- Usual slip
- Copying the angle
What your child learns in P5 parallelogram, rhombus and trapezium
Two skills, each with what it looks like on a worksheet.
See the syllabus wording
- properties of parallelogram, rhombus, trapezium
- finding unknown angles without additional construction of lines
Properties of a parallelogram, rhombus and trapezium
A parallelogram has two pairs of parallel sides, and opposite sides are equal. A rhombus is a parallelogram with four equal sides. A trapezium has one pair of parallel sides. Arrows mark parallel sides, ticks equal ones.
| Shape | Parallel sides | Equal sides |
|---|---|---|
| Parallelogram | 2 pairs | Opposite sides |
| Rhombus | 2 pairs | All 4 sides |
| Trapezium | 1 pair | Not always |
Find unknown angles from the marks
The properties are not written on the question, so your child reads them off the marks. In a parallelogram or a rhombus, opposite angles are equal and consecutive angles are supplementary: they add up to 180°. All four make 360°.
| Shape | Opposite angles | Angles next to each other |
|---|---|---|
| Parallelogram | Equal | Add up to 180° |
| Rhombus | Equal | Add up to 180° |
| Trapezium | Not always equal | Add up to 180° between the parallel sides |
Key facts and formulas
- ParallelogramOpposite sides parallel and equal. Angles next to each other add up to 180°.a →
- RhombusAll 4 sides equal. Opposite angles equal: a = 58°.
- TrapeziumOne pair of parallel sides. The angles between them add up to 180°.a →
Is a rhombus a parallelogram?
Yes. A rhombus has 2 pairs of parallel sides, so it is a special parallelogram, one with 4 equal sides. The shapes nest: every square is a rhombus, and every rhombus is a parallelogram.
A trapezium is not a parallelogram. In P5 it has one pair of parallel sides, so a shape with two pairs is never called a trapezium.
Words to know
- Parallelogram
- Two pairs of parallel sides. Opposite sides are equal, and opposite angles are equal.
- Rhombus
- A parallelogram with four equal sides. A square is a rhombus with right angles.
- Trapezium
- A four-sided shape with one pair of parallel sides.
- Parallel sides
- Sides that never meet. Matching arrows show them; matching ticks show equal sides.
- Opposite angles
- Angles across the shape from each other. In a parallelogram, they are equal.
- Consecutive angles
- Angles next to each other. In a parallelogram they are supplementary, adding up to 180°.
The sentence that costs the mark
A parallelogram has an angle of 70°. What is the angle next to it?
What the working usually does
same as70°=70°
Assumes the next angle is equal, the way the opposite one is. A parallelogram does have an equal pair, just not this pair.
What the question asked
180° −70°=110°
Consecutive angles add up to 180°, so the angle next to the 70° is 180° minus 70°.
A parallelogram really does have equal angles, so copying the 70° feels right. But the equal pair is the opposite angles. The angle next to it is consecutive, and consecutive angles add up to 180°. Both answers are real angles, so only knowing which pair is equal decides it.
The same P5 parallelogram, rhombus and trapezium question, worked properly
Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.
PQRS is a rhombus. PT is a straight line. ∠PQR = 64°. Find ∠SRT.
- In a rhombus, opposite angles are equal. The angle opposite the 64° at Q is at S, not at R, so ∠PSR = 64°.
- All four sides of a rhombus are equal, so SP = SR. Triangle PSR is isosceles, so its two base angles are equal.
- The angle sum of a triangle is 180°, so the base angles share 180° − 64° = 116°. So ∠PRS = 116° ÷ 2 = 58°.
- PRT is a straight line. Angles on a straight line add up to 180°, so ∠SRT = 180° − 58° = 122°.
- So the missing angle is 122°.
Every question in StudyLah comes with a walkthrough like this one.
Try it freeTwo quick P5 parallelogram, rhombus and trapezium questions
Try them together, then tap to check.
Question 1
PQRS is a trapezium. PQ is parallel to SR. ∠SPQ = 116°. Find ∠PSR.
Show answer
Answer64°. ∠SPQ and ∠PSR lie between the parallel sides, so they add up to 180°, and 180° − 116° = 64°.
Question 2
PQRS is a parallelogram. ∠PQR = 60° and ∠RPS = 45°. Find ∠QPR.
Show answer
Answer75°. Consecutive angles add up to 180°, so ∠QPS = 180° − 60° = 120°. Then ∠QPR = 120° − 45° = 75°.
Helping at home
How to tell it has clicked
You can check this without knowing the answer. Ask your child which angles in a parallelogram are equal. If they say the opposite ones, and that the angles next to each other add up to 180°, they have it. If they say the angle next to it matches, they have used a real rule on the wrong pair.
Try this tonight
Take a rectangular photo frame or box and push it so it leans into a parallelogram. As one corner opens wider, the corner next to it closes by the same amount, so the two always make 180°. Opposite corners stay matched; neighbours trade off.
Before and after P5 parallelogram, rhombus and trapezium
Builds on
Primary 3 Perpendicular and Parallel LinesSpots and draws parallel and perpendicular lines
Builds on
Primary 4 Rectangles and SquaresKnows which sides and corners must match
You are here
Primary 5 Parallelogram, Rhombus and Trapezium
Finds angles from parallel and equal sides
Head Start
How to prepare for PSLE Maths: P5 to P6 revisionOne of five P5 topics to revise before P6 Term 1
Leads to
Primary 6 Angles in Geometrical FiguresFinds unknown angles in composite figures
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See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.