SURYAMG - Lines and Angles Laboratory

Axiom 6.1 & 6.2 Engine

Intersection Plane

Lines AB and CD intersecting at point O

Vertically Opp. Pair 1 (∠AOC & ∠BOD) Vertically Opp. Pair 2 (∠COB & ∠AOD)

assessment Angle Measurement Lab

∠AOC (Indigo) 0°

∠COB (Emerald) 0°

∠BOD (Indigo) 0°

∠AOD (Emerald) 0°

Axiom 6.1: Linear Pair Check

∠AOC + ∠COB = 180°

Theorem 6.1: Vertically Opposite Check

∠AOC = ∠BOD

Try This: Click and drag the handles A or C on the canvas. Observe how adjacent angles always sum to exactly $180^\circ$ (supplementary), and opposite angles stay completely equal.

Exercise 6.2 Question 6 Physics Lab

Ray Reflection Construction Plot

Incident Ray AB || Reflected Ray CD

Incident & Reflected Rays Normal perpendicular lines (90°)

auto_stories Geometric Logic Proof

Angle of Incidence (∠1)

0.0°

Angle of Reflection (∠2)

0.0°

Incidence Corner (∠3)

0.0°

Reflection Corner (∠4)

0.0°

Theorems in Reflection Proof:

1. Law of Reflection:
At mirror PQ: ∠1 = ∠2
At mirror RS: ∠3 = ∠4

2. Normals Parallelism:
Since mirrors are parallel (PQ || RS), normal lines are parallel too (BE || CF).

3. Alternate Interior Connection:
Using transversal line segment BC, alternate interior angles are equal: ∠2 = ∠3.

4. Proving Alternate Rays:
Doubling both sides gives 2∠2 = 2∠3, which translates to the complete alternate angle equivalence: ∠ABC = ∠BCD.
Hence, incident ray AB is parallel to reflected ray CD!

Change Incident Direction 45° Inclined

Class 9 Mathematics — Chapter 6: Lines and Angles

assessment Angle Measurement Lab

style Theorems & Angle Pairs

auto_stories Geometric Logic Proof