Sheet № 219 · Foundation + Higher · AQA · Edexcel · OCR
Properties of Triangles –
Properties of triangles is a foundational GCSE Maths topic tested at both tiers on AQA, Edexcel, and OCR papers. You need to classify triangles by their sides and angles, recall the properties of each type, and use these properties to solve problems. This guide covers every triangle type with clear definitions, worked examples, and practi
§Key definitions
Question:
A triangle has sides of 5 cm, 5 cm, and 7 cm. Classify the triangle and find all its angles given that the angle opposite the 7 cm side is 88.9°.
Answer:
The triangle is an acute-angled isosceles triangle with angles 88.9°, 45.55°, and 45.55°.
Q1 (Foundation):
Classify a triangle with sides 6 cm, 8 cm, and 10 cm.
Q2 (Foundation):
An isosceles triangle has a base angle of 72°. Find the angle at the top.
Q3 (Higher):
A triangle has angles in the ratio 2 : 3 : 4. Find each angle and classify the triangle.
§Formulas to memorise
Angle sum of any triangle = 180°
Equilateral triangle: all sides equal, all angles = 60°, 3 lines of symmetry, rotational order 3
Isosceles triangle: 2 equal sides, 2 equal base angles, 1 line of symmetry
Look at the side lengths — are any equal? Are all equal?
If the triangle is equilateral, all angles are 60° and all sides are equal.
If isosceles, identify the two equal sides — the angles opposite them are equal.
Worked example
A triangle has sides of 5 cm, 5 cm, and 7 cm. Classify the triangle and find all its angles given that the angle opposite the 7 cm side is 88.9°.
Working:
⚠ Common mistakes
- ✗Assuming isosceles means two angles of 45°. The base angles are only 45° in a right-angled isosceles triangle. In general, isosceles means two angles are equal — their value depends on the triangle.
- ✗Confusing the equal sides with the equal angles. The equal angles are opposite the equal sides, not adjacent to them.
- ✗Forgetting that a right-angled triangle can also be isosceles. A triangle with angles 90°, 45°, 45° is both right-angled and isosceles.
✦ Exam tips
- →When justifying your answer in an exam, name the triangle type and state the property you used (e.g. "The triangle is isosceles because AB = AC, so angle ABC = angle ACB").
- →Mark equal sides with tick marks and equal angles with arcs on your diagram.
- →In circle geometry, two radii form an isosceles triangle — this is a very common setup.
- →Always verify your angles sum to 180°.