University:
High School
Course:
High School Geometry
Academic year:

2022
Views:

76

Pages:

6
Author:

Deon Odonnell

For Every Triangle 3 angles, 3 sides (no matter the size) Sum up to 180° (no matter the size) ∠1 + ∠2 + ∠3 = 180° If one ∠ = 90°, that forces the other angles to equal 90° together. ∠1 + ∠2 + 90° = 180° -90° -90° ∠1 + ∠2 = 90° For Every Right Triangle (90°) Pythagorean Theorem holds longest side: hypotenuse biggest angle = 90° a² + b² = c² Examples Example 1 Triangle with sides 4, 4, and x 4² + 4² = x² 16 + 16 = x² 32 = x² √32 = x 4√2 = x Example 2 Triangle with sides 6, 6, and x 6² + 6² = x² 36 + 36 = x² 72 = x² √72 = x 6√2 = x Example 3 Triangle with sides 7, 7, and x 7² + 7² = x² 49 + 49 = x² 98 = x² √98 = x 7√2 = x Example 4 Triangle with sides 4, b, and 8 4² + b² = 8² 16 + b² = 64 b² = 48 b = √48 b = 4√3 Example 5 Triangle with sides 3, a, and 6 3² + a² = 6² 9 + a² = 36 a² = 27 a = √27 a = 3√3 Special 45-45-90 Triangle with sides w, w, and w√2 Special 30-60-90 Triangle with sides w, w√3, and 2w