Lesson 1.3.1

Naming and Classifying Angles

Two rays sharing an endpoint create an angle. Learn how to name them correctly and classify them by their measure.

Introduction

Angles are everywhere — every corner of a room, every slice of pizza, every tick of a clock. Naming them precisely and classifying their size is foundational for everything that follows in geometry.

Past Knowledge

Rays and endpoints (1.1.2).

Today's Goal

Name angles using three-letter notation and classify them as acute, right, obtuse, or straight.

Future Success

Angle Addition (1.3.2), angle relationships (1.3.3-1.3.4), and every proof involving angles.

Key Concepts

What Is an Angle?

An angle is formed by two rays (the sides) that share a common endpoint (the vertex).

Naming Angles

  • Three letters: or — the vertex letter () is always in the middle.
  • By vertex alone: — only if there is no ambiguity (only one angle at that vertex).
  • By number: — when an angle is labelled with a number in a diagram.

Classifying by Measure

TypeMeasure
Acute
Right
Obtuse
Straight

Worked Examples

Basic

Naming an Angle

Two rays and share endpoint . Name the angle.

The vertex is , which goes in the middle.

Answer: (or ).

Intermediate

Classifying an Angle

Classify if .

, so the angle is between a right and a straight angle.

Answer: Obtuse.

Common Pitfalls

Vertex Not in the Middle

In three-letter notation, the vertex is always the middle letter. has vertex , not or .

Real-Life Applications

Clock Angles

At 3:00 the hour and minute hands form a 90° right angle. At 6:00 they form a 180° straight angle. Calculating the exact angle at any time combines rate-of-change thinking with angle classification.

Practice Quiz

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