Primary 4 Maths | Classifying Triangles by Sides and Angles, and the 180 Degree Check

2026-11-08

Tutor lesson-prep guides · Primary maths

Most pupils classify a triangle by how it looks: three sides that seem equal get called equilateral, any sharp corner gets called acute. This lesson takes the eye out of the decision and replaces it with two things that can be checked: measured sides and added angles.

Objectives — Pupils can: (1) sort triangles into equilateral, isosceles and scalene by side length; (2) sort them into acute, right and obtuse by the largest angle; (3) use the 180 degree angle sum to check whether their measured angles make sense.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Angle size	How many degrees in a right angle	90 degrees
Using a protractor	Where the centre of the protractor goes	On the vertex, with 0 on one side
Finding a missing angle	Two angles are 50 and 65; find the third	180 minus 50 minus 65, which is 65

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Opening question	Show three very flat triangles and ask which one is obtuse	Say what evidence they used
5-14 min	Sort by sides	Measure all three sides to the nearest mm, then name the triangle	Measure three triangles and record the sides
14-23 min	Sort by angles	Find the largest angle and compare it with 90 degrees	Mark the largest angle on each shape
23-33 min	Angle sum of 180	Add the three angles; the total must be 180, so it works as a check	Measure one triangle and add the angles
33-39 min	Both names at once	A triangle can be isosceles and right-angled at the same time	Write “isosceles right-angled triangle”
39-45 min	Exit check	Collect three questions and mark whether the error is sorting or measuring	Work independently

03 Teaching script (read it out)

Scene 1: Act 1: replace “it looks like” with “I measured it”

Set the rule at the start: “No eyes this lesson, only rulers.” Give each pupil a ruler and three triangles: a very flat isosceles one, a scalene one that looks almost equilateral, and a right-angled one. Ask them to write each side length on the side, to the nearest millimetre.
Only after that do they sort: three equal sides means equilateral, exactly two equal sides means isosceles, all different means scalene. Pupils must do: write the three lengths as “3, 4, 5” or “5, 5, 6” beside the shape, then write the name.

Tutor line: “You said it is equilateral: that was your eye talking, not the ruler. Tell me the three side lengths.”

Scene 2: Act 2: for angles, look at the largest one only

Sorting by angle needs just one angle, the largest. Use 90 degrees as the dividing line: below 90 is acute, exactly 90 is right-angled, above 90 is obtuse.
Explain why one angle is enough: the three angles add to 180, so if two angles were 90 or more they would already use up the whole 180 and leave nothing for the third. That is why a triangle can have at most one right angle and at most one obtuse angle.
Model it: angles 40, 60 and 80. The largest is 80, which is under 90, so the triangle is acute.

Tutor line: “You do not need all three. The largest one already tells you the family; the other two must be smaller than it.”

Scene 3: Act 3: 180 is a checking tool, not a sentence to memorise

Many pupils can recite “the angles add to 180” but never use it. Make it a compulsory step after every measurement: if the three angles do not add to 180, something was measured or read wrongly.
Worked example: an isosceles triangle with apex angle 40. The two base angles are equal, so (180 minus 40) divided by 2 gives 70 each, and 40 plus 70 plus 70 is 180.
Second example: a right-angled triangle with one acute angle of 28. The other acute angle is 180 minus 90 minus 28, which is 62. If a pupil measures 40, 70 and 75, do not let them adjust a number to fit: send them back to measure again, usually the wrong scale was read.

Tutor line: “The 180 is not for reciting, it is for catching mistakes. If the total is not 180, the measurement is wrong, not the triangle.”

Scene 4: Act 4: one shape can carry two names

A triangle is named by its sides and by its angles, and the two names do not clash. An isosceles right-angled triangle has two equal legs and two 45 degree acute angles, and 90 plus 45 plus 45 is 180. An equilateral triangle is also acute, because all three angles are 60.
Make one point precise: equilateral is a special case of isosceles, not the other way round. When a question asks “what must this triangle be”, use the most precise name.
Finish with the triangle inequality: any two sides must add to more than the third. Sides 3, 4 and 5 work because 3 plus 4 is more than 5; sides 2, 3 and 6 do not, because 2 plus 3 is less than 6. Let pupils cut drinking straws to these lengths and try it themselves.

Pupils must do: decide whether sides 5, 5 and 8 form a triangle, then give both classification names.

04 Question types and worked steps

Type	Example	Steps	Answer
Sort by sides	Sides 5, 5 and 6	Compare the three lengths: exactly two are equal	Isosceles
Sort by angles	Angles 40, 60 and 80	Largest angle compared with 90	Acute-angled
Missing base angle	Apex 40, isosceles	(180 minus 40) divided by 2	70 degrees
Can these sides form a triangle	2, 3 and 6	Add the two shorter sides and compare with the longest	No, 2 plus 3 is less than 6

Sanity check (teach this): After every measurement do two checks: the three angles must total 180 degrees, and there must be only one largest angle. If the total is 185 or 175, measure again rather than editing a number to reach 180. For sorting by sides, check that equilateral really has three equal sides and isosceles has exactly two.

05 Independent practice (3 questions)

Question	Answer	What to watch
An isosceles triangle has an apex angle of 40 degrees. Find each base angle.	70 degrees each	Did they divide by 2
A right-angled triangle has one acute angle of 28 degrees. Find the other acute angle.	62 degrees	Did they subtract 90 first
Can sides 5, 5 and 8 form a triangle? Give both classification names.	Yes; isosceles and acute-angled	Did they test two sides against the third

06 Common mistakes and what to say

Mistake	Student writes	Say this
Sorting by eye	Calling anything that looks even “equilateral”	No eyes: write the three lengths. Two equal is isosceles, three equal is equilateral
Calling isosceles equilateral	Writing 5, 5, 6 as equilateral	Equilateral needs three equal sides. Two equal is isosceles
Missing a right angle	Calling 90, 35 and 55 acute	A largest angle of exactly 90 makes it right-angled, not “almost acute”
Accepting angles that miss 180	Sorting 40, 70 and 75 without checking	That total is 185, so a measurement is wrong. Measure again, do not edit numbers

07 Homework (paper, section and question numbers)

Independent practice on this page (questions 1 to 3) — Question 1: show the division by 2; question 2: subtract 90 first; question 3: test two sides against the third
Primary maths test papers (shape and angle questions) — Do three shape questions, label every measured angle on the diagram, and write the 180 degree sum as a check
Primary maths chapter index (neighbouring topics) — Revise the P4 rectangle and square area chapter and compare how four-sided shapes differ from triangles

08 Exit check (last 5 minutes)

Question	Answer	Decision
What are the three names for triangles sorted by sides?	Equilateral, isosceles, scalene	Cannot say: return to Act 2
Which angle decides the angle-based name?	The largest one	Answering “all three” means the 180 sum is not understood
An isosceles triangle has apex 40. What are the base angles?	70 degrees each	Answering 140 means the division by 2 was missed
Angles measure 40, 70 and 75. What should you do?	Measure again, since the total is not 180	Answering without checking means Act 3 must be retaught

09 Tutor FAQ

Why is the largest angle enough for angle-based sorting?

Because the three angles of a triangle add to 180. If two angles were 90 or more, they alone would reach 180 and leave nothing for the third. So a triangle has at most one right angle or one obtuse angle, and the largest one decides the family.

My pupil keeps reading the wrong scale on the protractor. What helps?

Use one fixed sentence: centre on the vertex, zero on one side, read from zero on the same scale. Then ask them to say out loud whether they are reading the inner or outer scale. The 180 degree sum then acts as the final check, because a wrong scale shows up immediately.

How should I explain the link between isosceles and equilateral?

Equilateral is a special case of isosceles: all three sides equal automatically satisfies “two sides equal”. So an equilateral triangle may be called isosceles, but not the reverse. When a question asks what the triangle must be, give the most precise name.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.