Geometry is the study of shapes, sizes, positions, and properties of objects in space. Let's start with the fundamental concepts.
Point: Exact location (no size) • A
Line: Infinite straight path ↔
Ray: Line with one endpoint →
Angle: Formed by two rays with common endpoint
Triangle: 3 sides, 3 angles
Quadrilateral: 4 sides, 4 angles
Pentagon: 5 sides, 5 angles
Circle: All points equidistant from center
Angles are measured in degrees (°). Different angle sizes have special names.
Less than 90°
Example: 45°
Exactly 90°
Square corner
90° to 180°
Example: 120°
Exactly 180°
Straight line
When a transversal (crossing line) intersects parallel lines, it creates several angle relationships.
Corresponding Angles: Same position, equal
Alternate Interior: Inside, opposite sides, equal
Alternate Exterior: Outside, opposite sides, equal
Co-interior: Inside, same side, add to 180°
• Parallel lines never meet
• Corresponding angles are equal
• Alternate angles are equal
• Co-interior angles sum to 180°
Polygons have special rules for their interior and exterior angles.
Sum of Interior Angles:
(n - 2) × 180°
where n = number of sides
Each Interior Angle (Regular):
(n - 2) × 180° ÷ n
for regular polygons only
Triangle
Sum: 180°
Each: 60°
Square
Sum: 360°
Each: 90°
Pentagon
Sum: 540°
Each: 108°
Hexagon
Sum: 720°
Each: 120°
Exterior angles are formed when extending one side of a polygon.
• The sum of exterior angles of any polygon = 360°
• Each exterior angle of a regular n-sided polygon = 360° ÷ n
• Interior angle + exterior angle = 180° (linear pair)
1. What is the sum of interior angles in a pentagon?
Hint: Use (n - 2) × 180° where n = 5
°2. In a regular octagon, what is each interior angle?
Hint: Find total sum, then divide by number of angles
°3. If two parallel lines are cut by a transversal and one angle is 70°, what is the corresponding angle?
°