Geometry: Pairs of Angles

Interactive Learning with 3D Animations

Quick Reference Guide

📐 Linear Pair Axiom 6.1

Statement: If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.

∠AOC + ∠BOC = 180°

🔄 Linear Pair Axiom 6.2

Statement: If the sum of two adjacent angles is 180°, then the non-common arms form a line.

Note: This is the converse of Axiom 6.1

✖️ Theorem 6.1

Statement: If two lines intersect each other, then the vertically opposite angles are equal.

∠AOC = ∠BOD
∠AOD = ∠BOC

🎯 Adjacent Angles

Two angles are adjacent if they have:

• A common vertex

• A common arm

• Non-common arms on opposite sides

🔢 Angles Around a Point

Property: The sum of all angles around a point is 360°.

∠1 + ∠2 + ∠3 + ∠4 = 360°

📏 Practical Applications

• Architecture: Roof angles and support structures

• Engineering: Bridge design and truss systems

• Navigation: Bearing calculations