Basic Geometrical Ideas

A point marks a location. A line extends without end in both directions. A line segment has two endpoints, and a ray has one endpoint and goes on in one direction.

Parallel lines never meet; intersecting lines cross at a point.

What are Complementary Angles?

Two angles are complementary if their measures add up to 90°.

• Each angle is called the complement of the other
• They don't have to be adjacent (next to each other)

Example: 30° + 60° = 90° → Complementary

What are Supplementary Angles?

Two angles are supplementary if their measures add up to 180°.

• Each angle is called the supplement of the other
• They don't have to be adjacent

Example: 110° + 70° = 180° → Supplementary

COMPLEMENTARY ANGLES (sum = 90°):

    Adjacent Complementary:     Non-adjacent Complementary:
    
         /|
        / | 30°                    30°
       /  |                          60°
      /   | 60°
     /    |
    └─────┘
    
    30° + 60° = 90°             30° + 60° = 90°


SUPPLEMENTARY ANGLES (sum = 180°):

    Adjacent Supplementary (Linear Pair):   Non-adjacent:
    
        ┌─────────┐
        │         │
        │  120°   │       120°        60°
        │         │
        └─────────┘
    
    120° + 60° = 180°           120° + 60° = 180°


FINDING COMPLEMENTARY ANGLE:

    If one angle is 35°, complement = 90° - 35° = 55°
    If one angle is 72°, complement = 90° - 72° = 18°


FINDING SUPPLEMENTARY ANGLE:

    If one angle is 115°, supplement = 180° - 115° = 65°
    If one angle is 45°, supplement = 180° - 45° = 135°

A triangle has 3 sides, 3 vertices and 3 angles. In a circle, the centre is the middle, the radius is the centre-to-edge distance, the diameter goes across through the centre (= 2 × radius), and a chord joins two points on the circle.