Primary 5 · Measurement & Geometry

P5 properties of triangles

The properties of triangles start with one rule: the three angles add up to 180°. In P5, your child adds the isosceles, equilateral and right-angled triangles, and reads the tick marks that tell them apart.

Taught in
Term 4
Syllabus
3 skills
Usual slip
Forgetting to halve

An isosceles triangle with two equal sides and equal base angles

What your child learns in P5 properties of triangles

Three skills, each with what it looks like on a worksheet.

Follows the latest (2026) MOE syllabus
See the syllabus wording
  • properties of isosceles triangle, equilateral triangle, right-angled triangle
  • angle sum of a triangle
  • finding unknown angles without additional construction of lines

Isosceles, equilateral and right-angled

Tick marks show equal sides. An isosceles triangle has two equal sides, and the base angles opposite them are equal. An equilateral triangle has three equal sides, and every angle is 60°. A right-angled triangle has one right angle.

Isosceles
60°60°60°
Equilateral
Right-angled

The angle sum of a triangle

The three angles of any triangle add up to 180°. So when two angles are given, the third is what is left of 180°.

50°70°?
50° + 70° + 60° = 180°

Find unknown angles from the marks

Questions rarely say "isosceles". Your child reads the tick marks, works out which angles are equal, and writes the reason beside each line. No extra lines are drawn on the figure.

50°?
Equal sides, equal base angles

Key facts and formulas

Term 4
  • 65°48°a
    Angles in a triangleThey add up to 180°.180−65−48=180 - 65 - 48 = 67°67\degree
  • 65°65°a
    Isosceles triangle2 equal sides, 2 equal base angles.180−65−65=180 - 65 - 65 = 50°50\degree
  • 60°60°60°
    Equilateral triangle3 equal sides. Every angle is 60°.180÷3=180 \div 3 = 60°60\degree
  • 34°a
    Right-angled triangleThe other two angles add up to 90°.a → 90−34=90 - 34 = 56°56\degree

Words to know

Isosceles
A triangle with two equal sides. The base angles opposite them are equal.
Equilateral
A triangle with three equal sides. Every angle is 60°.
Base angles
The two equal angles of an isosceles triangle, opposite its equal sides.
Apex angle
The angle between the two equal sides of an isosceles triangle.
Tick marks
Small marks on sides that are equal in length.
Angle sum
The three angles of any triangle add up to 180°.

The sentence that costs the mark

An isosceles triangle has an apex angle of 40°, and its two equal sides carry matching tick marks. Find one of the base angles.

40°?
Two equal sides, so two equal base angles share what is left.

What the working usually does

all of180° − 40°=140°

Takes the whole leftover as a single base angle. It forgets that the equal sides mean two equal base angles that share the 140°.

What the question asked

half of180° − 40°=70°

Shares the leftover between the two equal base angles: 140° ÷ 2 = 70°. The tick marks on the equal sides are what say there are two of them.

Both start from the angle sum and both land on a real angle. The step that decides the mark is invisible in the arithmetic: whether the tick marks were read as two equal angles to share the remainder between.

The same P5 properties of triangles 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.

PQS is an equilateral triangle. PQR is an isosceles triangle where QP = QR and ∠RQS = 50°. Find ∠PRQ.

PQRS50°?
Step 1 of 5▌
  1. PQS is an equilateral triangle, so each of its angles is 60°.
  2. Chase the angle at Q. The angle of 50° sits beside it, so ∠PQR = 60° + 50° = 110°.
  3. QP = QR, so triangle PQR is isosceles. The angle sum of a triangle leaves 180° − 110° = 70° for its two base angles.
  4. That 70° belongs to two equal base angles, so ∠PRQ = 70° ÷ 2 = 35°.
  5. So the missing angle is 35°.

Every question in StudyLah comes with a walkthrough like this one.

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Two quick P5 properties of triangles questions

Try them together, then tap to check.

Question 1

EFG is an isosceles triangle and H is a point on FG. ∠EGF = 50° and ∠HEG = 32°. Find ∠FEH.

EFGH50°32°?
Show answer

Answer48°. EF = EG, so ∠EFG = 50° too, and ∠FEG = 180° − 50° − 50° = 80°. So ∠FEH = 80° − 32° = 48°.

Question 2

Triangle B has a right angle. Is it an isosceles triangle?

Show answer

AnswerNot possible to tell. Nothing is said about its sides, so its angles could be 45°, 45° and 90°, or 30°, 60° and 90°.

Helping at home

How to tell it has clicked

You do not need to do the angle maths to check this. When a triangle has tick marks on two sides, ask how many equal angles that makes. A child who says two equal base angles, and shares the leftover between them, has it.

Try this tonight

Fold a rectangular sheet of paper corner to corner and cut along the fold. The two halves are identical, and their matching corners are equal. Point at the matching corners and ask what must be true about them: equal sides force equal angles.

Before and after P5 properties of triangles

  1. Builds on

    Primary 5 Angles

    Finds unknown angles on lines and points

  2. You are here

    Primary 5 Properties of Triangles

    Uses equal sides to find equal angles

  3. Head Start

    How to prepare for PSLE Maths: P5 to P6 revision

    One of five P5 topics to revise before P6 Term 1

  4. Leads to

    Primary 6 Angles in Geometrical Figures

    Finds unknown angles in composite figures

In the PSLE's hardest questions

More in Primary 5

Struggling with the working rather than the topic itself? How to help your child with problem sums

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.

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