Triangles: Pythagoras, Angles and Congruence
Triangle geometry combines angle sums, right-triangle calculations and tests for congruence.
Key facts
The angles in a triangle sum to 180°. In a right-angled triangle, Pythagoras gives c² = a² + b², where c is the hypotenuse. Congruent triangles have the same shape and size; valid tests include SSS, SAS, ASA and RHS.
Parallel lines and angles
When a transversal crosses parallel lines, alternate angles are equal and corresponding angles are equal. Co-interior angles sum to 180°.
Worked examples
- A right triangle with legs 6 cm and 8 cm has c = √(36+64) = 10 cm.
- If two angles are 48° and 72°, the third is 60°.
- Two triangles with three matching side lengths are congruent by SSS.
Practice
- Find the hypotenuse when the legs are 5 cm and 12 cm.
- Find the missing angle in a triangle with angles 35° and 85°.
- State a congruence test for two right-angled triangles.
