Geometry Rules Flashcards

Straight Line Angles

• Angles on a straight line total 180⁰.

Triangle Angle Sum

• The sum of all angles in any triangle (∆) equals 180⁰.

Polygon Interior Angles

• Interior angles of a polygon total (n-2)×180, where n equals the number of sides and (n-2) represents the number of triangles formed.

Polygon Exterior Angles

• The sum of the exterior angles of any polygon is always 360⁰, with one exterior angle per vertex.

Corresponding Angles

• Each exterior angle corresponds with its interior angle for a total of 180⁰, creating a straight line.

Triangle Exterior Angle Rule

• An exterior angle of a triangle equals the sum of its two opposite interior angles.

Triangle Area

• Area of a triangle is calculated using the formula 1/2bh (base × height).

Pythagorean Theorem

• In right triangles, a² + b² = c², where c is the hypotenuse. If this holds true, the triangle is right-angled; if not, it's not.

30-60-90 Triangle

• In a 30⁰: 60⁰: 90⁰ triangle, the leg lengths follow the ratio x: x√3: 2x, with x opposite the 30⁰ angle and 2x opposite the 90⁰ angle.

45-45-90 Triangle

• A right isosceles triangle (45⁰: 45⁰: 90⁰) has leg lengths in the ratio x: x: x√2. The hypotenuse can be set to √2 for calculation or halved and multiplied by √2.

3-4-5 Triangle Rule

• Classic Pythagorean triples include 3-4-5 ∆ (3² + 4² = 5²) and 5-12-13 ∆ (5² + 12² = 13²), with common multiples like 6:8:10.

Triangle Inequality Theorem

• The length of the third side of any triangle must be greater than the absolute difference of the other two sides and less than their sum.

3-4-5 Triangle Family

• Related triples include 6:8:10, 9:12:15, 12:16:20, and 15:20:25, all derived from the 3-4-5 relationship.