How is classifying by angles different from by sides?

By angles you look at the largest angle; by sides you count how many sides are equal.

How do isosceles and equilateral triangles relate?

Every equilateral triangle is also isosceles, but not every isosceles triangle is equilateral.

Why is the angle sum 180°?

At P4 you just use the result: subtract the two known angles from 180° to find the third.

P4 Maths Classifying Triangles Paper 3: Challenge

2026-11-09

Tutor Prep Guide · P4 Maths

Ten original items, each with an answer and a one-line explanation.

Direct answers　Items 1-3 are basic, 4-6 intermediate and 7-9 challenge, with item 10 as the error review. Time yourself first, then check each answer and redo what is wrong.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: P4 Maths Classifying Triangles
Level	P4

02　Questions (10 items)

FoundationThe angles of a triangle are in the ratio 1 : 2 : 3. Find the three angles.
FoundationIn an isosceles triangle the apex angle is twice a base angle. Find both.
FoundationTwo angles of a triangle differ by 20° and the smaller is 50°. Find the third angle.
IntermediateCan a triangle have sides 5 cm, 5 cm and 10 cm? Why?
IntermediateAn equilateral triangle has side 9 cm. What is its perimeter?
IntermediateAn isosceles triangle has perimeter 40 cm and base 10 cm. How long is each equal side?
ChallengeIn a right-angled triangle one acute angle is four times the other. Find both.
ChallengeOne angle of a triangle is 90° and the other two are equal. Find them and name the triangle.
ChallengeThe largest angle is three times the smallest and the middle angle is 60°. Find the smallest and largest.
Error redoError review: a pupil says every isosceles triangle is acute-angled. Is that right?

03　Answers and one-line notes

#	Answer	One-line note
1	30°, 60° and 90°	180 divided by 6 = 30, giving 30°, 60° and 90°; the largest is 90°, so it is right-angled.
2	base 45°, apex 90°	Let the base angle be x: x + x + 2x = 180, so 4x = 180 and x = 45, giving an apex of 90°.
3	60 degrees	The larger angle is 50 + 20 = 70°, so the third is 180 minus 50 minus 70 = 60 degrees.
4	No	The two shorter sides add to 5 + 5 = 10, which only equals the third side, so the triangle cannot close.
5	27 cm	Three equal sides give 9 times 3 = 27 cm.
6	10 cm	The two equal sides share 40 minus 10 = 30 cm, so each is 30 divided by 2 = 10 cm.
7	18° and 72°	The acute angles total 90°: 5x = 90, so x = 18 and the other is 72°.
8	18° each, an isosceles right-angled triangle	(180 minus 90) divided by 2 = 18°, so each is 18° and the triangle is an isosceles right-angled triangle.
9	smallest 30°, largest 90°	Let the smallest be x: x + 3x + 60 = 180, so 4x = 120, x = 30 and the largest is 90°.
10	No, an isosceles triangle can also be right-angled or obtuse-angled	For example 90°, 45°, 45° is an isosceles right-angled triangle and 120°, 30°, 30° is isosceles obtuse, so the claim is false.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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