Triangles — O/L Mathematics

What must I remember about Triangles?

• Angle sum of a triangle theorem: The sum of the three interior angles of any planar triangle is always 180°.
• Exterior angle theorem: An exterior angle formed by producing one side of a triangle equals the sum of the two interior opposite angles.
• Isosceles triangle properties: The angles opposite to the equal sides are equal; the perpendicular bisector from the apex bisects the base and apex angle.
• Equilateral triangle properties: All three sides are equal, and all three interior angles measure exactly 60°.
• Triangle inequality theorem: The sum of the lengths of any two sides of a triangle must always be strictly greater than the length of the third side.

Test yourself (1 minute)

1. Exterior angle misidentification trap

   The exterior angle is formed between the produced line and the adjacent side, NOT the reflex angle or vertical opposite angle.

2. Proof justification in angle-chasing problems

   In Paper 1 Part A, always cite geometric theorems concisely (e.g., 'ext. angle of △', 'angles on a straight line = 180°', 'angles opposite equal sides').

3. Triangle existence check

   To verify if side lengths (a, b, c) can form a triangle, verify that the sum of the two smaller sides exceeds the longest side.

Practise Triangles questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 8)

What should I study first?

What comes next?

Next in the syllabus

Where does Triangles fit in the syllabus?

Grade 10 · Term 1