Unit 3 · Geometry and Measurement · Lesson Four
The Triangle
Three rules govern every triangle you will ever draw: its angles always total 180°, each exterior angle equals the two far interior angles, and its three sides must satisfy the triangle inequality. This site explains each one with diagrams, proofs, examples and games.
Learning Outcomes
- • Deduce the sum of the interior angles of a triangle.
- • Learn the concept of the exterior angle of a triangle.
- • Deduce the relationship between an exterior angle and the interior angles.
- • Learn the concept of the triangle inequality.
Vocabulary
- Interior angle
- An angle formed inside the triangle by two of its sides.
- Exterior angle
- The angle between one side and the extension of an adjacent side.
- Triangle inequality
- The sum of any two side lengths is greater than the third side length.
Lesson Map
Sum of Interior Angles
Why every triangle's angles add to 180°, with the parallel-lines proof and worked examples.
02The Exterior Angle
What counts as an exterior angle, and why it equals the sum of the two non-adjacent interior angles.
03Triangle Inequality
When three lengths can form a triangle — ruler-and-compass activity and the quick test.
04Exercise 14
Full exercise set: complete, find the variable, proofs, problem solving and multiple choice.
05Activities & Games
Missing Angle Sprint, Triangle Builder, Exterior Angle Challenge and a quiz arena.