This topic summary covers Knowledge Organiser: Properties of Triangles within Properties of Triangles for GCSE Mathematics. Revise Properties of Triangles in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 9 of 9 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Properties of Triangles
Key Terms
- Equilateral: All 3 sides equal, all angles 60°
- Isosceles: 2 equal sides, 2 equal base angles
- Scalene: All sides and angles different
- Right-angled: One angle exactly 90°
- Exterior angle: Angle outside the triangle at a vertex
- Hypotenuse: Longest side, opposite the right angle
Must-Know Facts
- Angles in any triangle sum to 180°
- Equilateral triangle: all angles = 60°, 3 lines of symmetry
- Isosceles: the two base angles (opposite equal sides) are equal
- Exterior angle = sum of the two opposite interior angles
- A right-angled triangle's two acute angles sum to 90°
- Tick marks show equal sides; arc marks show equal angles
Key Methods
- Missing angle: a + b + x = 180°, solve for x
- Isosceles missing angle: apex + 2x = 180°
- Exterior angle shortcut: ext = sum of opposite two interiors
- Always state reason: "angles in a triangle sum to 180°"
Common Mistakes
- Forgetting that isosceles base angles are equal: If two sides are equal, the base angles opposite them are equal — mark both angles before writing an equation
- Exterior angle confusion: The exterior angle of a triangle equals the sum of the two NON-adjacent interior angles — not just one of them
- Assuming all triangles are right-angled: Only apply Pythagoras or SOH CAH TOA when there is a right angle — always check the diagram
- Not stating the reason: Geometry proofs and angle-chase questions require the rule written out — "angles in a triangle sum to 180°" earns a mark on its own
Practice questions for Properties of Triangles
What is the sum of the interior angles of any triangle?
Describe the key properties of an equilateral triangle. State two properties relating to sides and two relating to angles.
Quick recall flashcards
Triangle Angle Sum
Always 180°
Isosceles Triangle
Two equal sides, two equal angles