Grade 9 Geometry & Trigonometry – Complete Study Guide

Grade 9 Geometry & Trigonometry –
Complete Study Guide
This document covers EVERY essential concept you need for Grade 9 Geometry and
Trigonometry, written cleanly so you can paste it into Google Docs.




1. Basic Geometry Foundations
1.1 Points, Lines, and Planes
●​ Point: a location in space (no size).​

●​ Line: infinite length, no thickness.​

●​ Line Segment: part of a line with two endpoints.​

●​ Ray: has one endpoint, extends infinitely in one direction.​

●​ Plane: a flat surface extending infinitely.​



1.2 Types of Angles
●​ Acute: < 90°​

●​ Right: = 90°​

●​ Obtuse: 90°–180°​

●​ Straight: = 180°​

●​ Reflex: > 180°​



1.3 Angle Pair Relationships

, ●​ Vertical Angles: equal angles across intersecting lines.​

●​ Adjacent Angles: share a side.​

●​ Complementary: sum to 90°.​

●​ Supplementary: sum to 180°.​



Parallel line angle relationships

●​ Corresponding Angles → equal.​

●​ Alternate Interior Angles → equal.​

●​ Alternate Exterior Angles → equal.​

●​ Co-interior angles → sum to 180°.​




2. Triangles
2.1 Triangle Types by Sides
●​ Scalene: all sides different.​

●​ Isosceles: 2 equal sides.​

●​ Equilateral: all equal.​



2.2 Triangle Types by Angles
●​ Acute Triangle: all angles < 90°.​

●​ Right Triangle: has a 90° angle.​

●​ Obtuse Triangle: has > 90° angle.​