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.
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.
