Geometric Angle Relationships and Formulas

This page presents a comprehensive overview of fundamental geometric concepts related to angles in various shapes. It covers essential formulas and rules for understanding angle relationships in triangles, quadrilaterals, and polygons.

Highlight: The document provides a quick reference guide for key angle facts and formulas in geometry.

Triangle Angles

The page begins by discussing angles in triangles:

Definition: Angles in a triangle add up to 180°.

This is a fundamental principle in geometry. The document also mentions specific types of triangles:

Vocabulary: In an isosceles triangle, the base angles are equal.

Example: In an equilateral triangle, all angles are equal and measure 60°.

Quadrilateral Angles

Moving on to quadrilaterals, the document states:

Definition: Angles in a quadrilateral add up to 360°.

This is another crucial concept in geometry, applicable to all four-sided shapes.

Angles on Lines and Around Points

The page covers several important angle relationships:

1. Angles on a straight line add up to 180°.
2. Angles around a point add up to 360°.
3. Vertically opposite angles are equal.
4. Alternate angles are equal (Z-rule).
5. Corresponding angles are equal (F-rule).
6. Supplementary angles add up to 180° (C-rule).

These relationships are fundamental in understanding angle properties in various geometric configurations.

Polygon Angles

The document concludes with formulas for angles in polygons:

Definition: The sum of exterior angles of a polygon is always 360°.

Highlight: Sum of interior angles of a polygon formula: (n-2) × 180°, where n is the number of sides.

Vocabulary: For a regular polygon, the exterior angle formula is 360° ÷ n, where n is the number of sides.

Definition: The interior angle of a regular polygon formula is [(n-2) × 180°] ÷ n.

Lastly, it notes that for any polygon, the sum of an interior angle and an exterior angle at the same vertex is always 180°.

This comprehensive guide serves as an excellent resource for students studying geometry, providing essential formulas and concepts for understanding angle relationships in various shapes.