Lines, Angles, and Triangles
1. Interior Angle Sum
All triangles have interior angles that sum to 180°.
For polygons: sum = \((n - 2) \times 180^\circ\), where \(n\) is the number of sides.
2. Complementary & Supplementary Angles
- Complementary angles add to 90°
- Supplementary angles add to 180°
3. Vertical Angles
Vertical angles are equal (opposite angles made by two intersecting lines).
4. Exterior Angle Rule
The exterior angle of a triangle equals the sum of the two remote interior angles.
5. Triangle Angle & Side Properties
- Sides are proportional to their opposite angles.
- Isosceles triangles have two equal angles and sides.
- 30-60-90 triangles follow a special ratio.
6. Alternate Interior & Corresponding Angles
When parallel lines are cut by a transversal, alternate interior and corresponding angles are equal.
7. Similar Triangles
- AA, SSS, SAS are criteria for triangle similarity.
- Parallel line extension creates similar triangles.
- SSA is not a valid similarity rule.
- Special right triangles include 45-45-90, 30-60-90, and Pythagorean triples.
