Learning Objectives
- Classify triangles by sides and angles
- Understand the angle sum property of triangles
- Learn the exterior angle property
- Apply the triangle inequality property
- Know properties of special triangles (equilateral, isosceles, right-angled)
Key Concepts
Angle Sum Property
The sum of all three interior angles of a triangle is always 180°.
If angles are A, B, C then: A + B + C = 180°
Exterior Angle Property
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Exterior angle = Sum of two remote interior angles
Triangle Inequality Property
The sum of any two sides of a triangle must be greater than the third side.
If sides are a, b, c then: a + b > c, b + c > a, a + c > b
Types of Triangles
By sides: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (no sides equal)
By angles: Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°)
Pythagoras Theorem (Right Triangle)
In a right-angled triangle: Hypotenuse² = Base² + Height²
Summary
Triangles have fundamental properties including the angle sum property (180°), exterior angle property, and triangle inequality. The Pythagoras theorem applies to right triangles. Medians, altitudes, and angle bisectors are important elements of a triangle.
Important Terms
- Median
- A line segment joining a vertex to the midpoint of the opposite side
- Altitude
- The perpendicular distance from a vertex to the opposite side
- Hypotenuse
- The longest side of a right triangle, opposite the right angle
- Equilateral Triangle
- A triangle with all three sides equal and each angle measuring 60°
Quick Revision
- Sum of angles in a triangle = 180°
- Exterior angle = Sum of two opposite interior angles
- Sum of any two sides > Third side
- In a right triangle: Hypotenuse² = Base² + Perpendicular²
- An equilateral triangle has all angles = 60°
- An isosceles triangle has two equal sides and two equal base angles
Practice Tips
- Construct different types of triangles using ruler and compass
- Verify the Pythagoras theorem by measuring sides of right triangles
- Try forming triangles with given side lengths to test the inequality property