P5 Quadrilaterals: The 3 Shapes You Must Know for PSLE

Parallelogram, Rhombus, Trapezium — three shapes, a handful of angle rules, and you can solve every P5 quadrilateral question. This guide walks you through each shape, its properties, and 10 worked examples so nothing catches you off guard on exam day.

First Things First: What Is a Quadrilateral?

A quadrilateral is any 4-sided shape. The angles inside every quadrilateral always add up to 360°.

$\text{Sum of angles in a quadrilateral} = 360°$

You already know squares and rectangles from earlier levels. In P5, you meet three new members of the quadrilateral family:

Shape	Key Feature
Parallelogram	2 pairs of parallel sides
Rhombus	4 equal sides (special parallelogram)
Trapezium	Exactly 1 pair of parallel sides

💡 The Shape Family Tree

Every rhombus is a parallelogram (it has 2 pairs of parallel sides AND all sides equal). But not every parallelogram is a rhombus — a regular parallelogram only needs opposite sides equal.

Part 1: The Parallelogram

A parallelogram has 2 pairs of parallel sides. Look for the small arrow markers on the diagram — matching arrows mean those sides are parallel.

The 3 Parallelogram Rules

Rule	Property
Rule 1	Opposite sides are equal in length
Rule 2	Opposite angles are equal
Rule 3	Adjacent angles (neighbours) add up to 180°

Rule 2: Opposite Angles Are Equal

Angles that sit diagonally across from each other are always equal.

If ∠A = 70°, then ∠C = 70° (they are opposite).

Example 1: Find the Opposite Angle

Problem:

In parallelogram PQRS, ∠P = 70°. Find ∠R.

Solution:

∠P and ∠R are opposite angles in a parallelogram.

Opposite angles are equal.

$\angle R = \angle P = 70°$

Example 2: Using the Variable

Problem:

In parallelogram JKLM, ∠J = 65°. Find the value of angle y if ∠L = y.

Solution:

∠J and ∠L are opposite angles.

$y = 65°$

Rule 3: Adjacent Angles Sum to 180°

Angles that are next to each other (they share a side) always add up to 180°. This is because the two parallel sides act like parallel lines, and the shared side is a transversal — making these co-interior angles.

Example 3: Find the Adjacent Angle

Problem:

ABCD is a parallelogram. ∠A = 80°. Find ∠B.

Solution:

∠A and ∠B are adjacent angles (neighbours).

Adjacent angles in a parallelogram sum to 180°.

$\angle B = 180° - 80° = 100°$

Example 4: Find All Four Angles

Problem:

In parallelogram WXYZ, ∠W = 120°. Find ∠X, ∠Y, and ∠Z.

Solution:

Step 1: ∠Y is opposite to ∠W.

$\angle Y = 120°$

Step 2: ∠X is adjacent to ∠W.

$\angle X = 180° - 120° = 60°$

Step 3: ∠Z is opposite to ∠X (or adjacent to ∠W — either method works).

$\angle Z = 60°$

Check: $120° + 60° + 120° + 60° = 360°$ ✓

⚠️ Common Mistake: Mixing Up Opposite and Adjacent

Students sometimes subtract from 180° when they should just copy the angle (opposite), or copy the angle when they should subtract (adjacent). Always identify the relationship first — are the two angles across from each other or next to each other?

Part 2: The Rhombus

A rhombus is a special parallelogram where all 4 sides are equal. Think of it as a “tilted square” or a diamond shape.

Rhombus Rules

Since a rhombus is a parallelogram, it inherits all three parallelogram rules PLUS one extra:

Rule	Property
Rule 1	All 4 sides are equal
Rule 2	Opposite angles are equal
Rule 3	Adjacent angles sum to 180°
Rule 4	Diagonals bisect (cut in half) the vertex angles

Example 5: Rhombus Side Length

Problem:

In rhombus PQRS, PQ = 5 cm. What is the length of RS?

Solution:

All sides of a rhombus are equal.

$PQ = QR = RS = SP = 5 \text{ cm}$

$RS = 5 \text{ cm}$

Example 6: Rhombus Angles

Problem:

In rhombus EFGH, ∠E = 100°. Find ∠F.

Solution:

∠E and ∠F are adjacent angles.

Adjacent angles sum to 180° (same as a parallelogram).

$\angle F = 180° - 100° = 80°$

Example 7: Rhombus Diagonal Bisects Angle

Problem:

ABCD is a rhombus. Diagonal AC cuts ∠A into two equal parts. If ∠DAC = 35°, find ∠D.

Solution:

Step 1: The diagonal bisects ∠A, so:

$\angle A = 35° + 35° = 70°$

Step 2: ∠D and ∠A are adjacent angles.

$\angle D = 180° - 70° = 110°$

💡 Rhombus vs Parallelogram — What's Different?

The angle rules are identical. The only difference is that a rhombus has 4 equal sides and its diagonals bisect the vertex angles. If a question doesn’t mention side lengths or diagonals, solve it the same way as a parallelogram.

Part 3: The Trapezium

A trapezium is the odd one out — it has exactly 1 pair of parallel sides. The parallel sides are called the top and bottom (or the two bases).

Trapezium Rules

Rule	Property
Rule 1	Exactly 1 pair of parallel sides
Rule 2	Co-interior angles (between the parallel sides, on the same side) sum to 180°

What Are Co-interior Angles?

Co-interior angles sit between the two parallel lines, on the same side of the transversal. In a trapezium, the non-parallel sides act as transversals.

$\text{Co-interior angle pair: } \angle \text{top-left} + \angle \text{bottom-left} = 180°$ $\text{Co-interior angle pair: } \angle \text{top-right} + \angle \text{bottom-right} = 180°$

Example 8: Find a Trapezium Angle

Problem:

In trapezium PQRS, PQ // SR. If ∠P = 110°, find ∠S.

Solution:

∠P and ∠S are co-interior angles (between the parallel sides, on the left side).

Co-interior angles sum to 180°.

$\angle S = 180° - 110° = 70°$

Example 9: Isosceles Trapezium

Problem:

ABCD is an isosceles trapezium with AB // DC. The non-parallel sides AD and BC are equal. If ∠D = 70°, find ∠A.

Solution:

∠A and ∠D are co-interior angles (between the parallel sides).

$\angle A = 180° - 70° = 110°$

Bonus fact: In an isosceles trapezium, angles at each parallel side are equal:

∠C = ∠D = 70° (both at the top)
∠A = ∠B = 110° (both at the bottom)

⚠️ Trapezium ≠ Parallelogram

A trapezium only has one pair of parallel sides. The co-interior angle rule only works for angles on the same side between the parallel lines. You cannot say opposite angles are equal in a trapezium (unless it happens to be isosceles — and even then, it’s only angles at the same base).

Challenge: Combining Rules

The toughest P5 questions mix quadrilateral properties with triangle angle rules. Here’s how to handle them.

Example 10: Parallelogram + Triangle

Problem:

PQRS is a parallelogram. A diagonal QS divides it into two triangles. In triangle QRS, ∠QSR = 40° and ∠R = 110°. Find ∠RQS.

Solution:

Focus on triangle QRS. The angles in a triangle sum to 180°.

$\angle RQS + \angle R + \angle QSR = 180°$

$\angle RQS + 110° + 40° = 180°$

$\angle RQS = 180° - 150°$

$\angle RQS = 30°$

Example 11: Trapezium with Algebra

Problem:

A trapezium has co-interior angles x and 2x. Find the value of x.

Solution:

Co-interior angles sum to 180°.

$x + 2x = 180°$

$3x = 180°$

$x = 60°$

Understanding how these shapes relate to each other helps you decide which rules to use:

        Quadrilateral (4 sides, angles sum = 360°)
              /                    \
    Trapezium                 Parallelogram
    (1 pair parallel)       (2 pairs parallel)
                                  |
                              Rhombus
                          (4 equal sides)
                                  |
                              Square
                     (4 equal sides + 4 right angles)

💡 Use the Hierarchy on Exam Day

If a question says “ABCD is a rhombus”, you can use ALL parallelogram rules too — because every rhombus is a parallelogram. But if it says “ABCD is a trapezium”, you can only use the co-interior angle rule, NOT the opposite-angles-equal rule.

5 Common Mistakes to Avoid

Mistake 1: Using Opposite Angles Rule on a Trapezium

A trapezium does not have equal opposite angles (unless it’s isosceles, and even then only the base angles match). Only parallelograms and rhombuses have this property.

Mistake 2: Forgetting the Co-interior Rule

When you see a trapezium and two angles on the same side, they add up to 180°. Students sometimes try 360° ÷ 4 = 90° instead — that only works for rectangles and squares!

Mistake 3: Mixing Up “Opposite” and “Adjacent”

In parallelogram ABCD going clockwise:

Opposite pairs: ∠A & ∠C, ∠B & ∠D → equal
Adjacent pairs: ∠A & ∠B, ∠B & ∠C, ∠C & ∠D, ∠D & ∠A → sum to 180°

Mistake 4: Assuming All Sides Are Equal

Only a rhombus (and a square) has 4 equal sides. A regular parallelogram only has opposite sides equal.

Mistake 5: Not Writing the Property Name

Always state the rule in your working:

“Opposite angles of a parallelogram are equal.”
“Co-interior angles between parallel lines sum to 180°.”

This earns you method marks even if you make a calculation slip.

Explore Angle Sums with the Polygon Calculator

Use the calculator below to check that a quadrilateral (4 sides) always has interior angles summing to 360°. Try other polygons too!

Polygon Calculator

Number of Sides (n)

Min: 3 sides

Quick Reference Card

Print this out or screenshot it for your revision!

Parallelogram

2 pairs of parallel sides
Opposite sides equal
Opposite angles equal
Adjacent angles sum to 180°

Rhombus

4 equal sides (special parallelogram)
All parallelogram rules apply
Diagonals bisect vertex angles

Trapezium

1 pair of parallel sides
Co-interior angles sum to 180°
Isosceles trapezium: base angles equal

Universal Rule

Angles in any quadrilateral sum to 360°

What to Practise Next

Now that you know the properties, put them to work:

P5 Angles — combine quadrilateral rules with straight-line and vertically-opposite-angle questions
Finding unknown angles — multi-step problems mixing triangles and quadrilaterals
Past-year PSLE questions — geometry questions often combine 2–3 rules in one diagram

Ready to Practise Quadrilateral Questions?

Our AI tutor walks you through parallelogram, rhombus, and trapezium problems step by step — and gives hints when you’re stuck.

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P5 Quadrilaterals: Parallelogram, Rhombus & Trapezium Guide

P5 Quadrilaterals: The 3 Shapes You Must Know for PSLE

First Things First: What Is a Quadrilateral?

Part 1: The Parallelogram

The 3 Parallelogram Rules

Rule 2: Opposite Angles Are Equal

Rule 3: Adjacent Angles Sum to 180°

Part 2: The Rhombus

Rhombus Rules

Part 3: The Trapezium

Trapezium Rules

What Are Co-interior Angles?

Challenge: Combining Rules

5 Common Mistakes to Avoid

Mistake 1: Using Opposite Angles Rule on a Trapezium

Mistake 2: Forgetting the Co-interior Rule

Mistake 3: Mixing Up “Opposite” and “Adjacent”

Mistake 4: Assuming All Sides Are Equal

Mistake 5: Not Writing the Property Name

Explore Angle Sums with the Polygon Calculator

Polygon Calculator

Quick Reference Card

Parallelogram

Rhombus

Trapezium

Universal Rule

What to Practise Next

Ready to Practise Quadrilateral Questions?

Topics covered:

Want personalized AI tutoring?

P5 Quadrilaterals: The 3 Shapes You Must Know for PSLE

First Things First: What Is a Quadrilateral?

Part 1: The Parallelogram

The 3 Parallelogram Rules

Rule 2: Opposite Angles Are Equal

Rule 3: Adjacent Angles Sum to 180°

Part 2: The Rhombus

Rhombus Rules

Part 3: The Trapezium

Trapezium Rules

What Are Co-interior Angles?

Challenge: Combining Rules

The Shape Hierarchy: How They’re Related

5 Common Mistakes to Avoid

Mistake 1: Using Opposite Angles Rule on a Trapezium

Mistake 2: Forgetting the Co-interior Rule

Mistake 3: Mixing Up “Opposite” and “Adjacent”

Mistake 4: Assuming All Sides Are Equal

Mistake 5: Not Writing the Property Name

Explore Angle Sums with the Polygon Calculator

Polygon Calculator

Quick Reference Card

Parallelogram

Rhombus

Trapezium

Universal Rule

What to Practise Next

Ready to Practise Quadrilateral Questions?

Topics covered:

Want personalized AI tutoring?