Triangles

Board: GSEB Class: 9

Chapter Overview

Two triangles are congruent if they are identical in shape and size. Congruence criteria: SSS (three sides equal), SAS (two sides and included angle equal), ASA (two angles and included side equal), RHS (right angle-hypotenuse-side). Properties of isosceles triangles: angles opposite equal sides are equal, and conversely. Triangle inequalities: the sum of any two sides is greater than the third side. The difference of any two sides is less than the third side.

Topics Covered

Congruence Definition
SSS Congruence
SAS Congruence
ASA Congruence
RHS Congruence
Isosceles Triangle Properties
Inequalities in Triangles
Triangle Proofs

Key Formulas

SSS: AB = DE, BC = EF, CA = FD

SAS: AB = DE, A = D, AC = DF

ASA: A = D, AB = DE, B = E

Isosceles: AB = AC => B = C

Triangle inequality: AB + BC > AC

Real-World Applications

Applications: Architecture, bridge design, construction, trigonometry foundations, structural engineering.

Study Tips

Tip: Learn all four congruence criteria

Tip: Practice writing proofs in logical order

Tip: Remember the difference between congruence and similarity