Congruence Test – O Level Exam Preparation Guide

In this Congruence Test revision note, you will learn the steps for different congruence tests and the properties of Congruent triangles.

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congruence test notes

 

Congruent Figures

  • Two geometric figures are congruent if they are of the same shape and size.
  • When two figures undergoes a rotation, reflection, or translation, the shape and size remains the same. Hence, they are congruent to each other.

congruent triangles

Congruent triangles properties

ΔABC ≡ ΔDEF (Note that the order matters)

if and only if…

corresponding sides are equal,

AB = DE , AC = DF and BC = EF

and corresponding angles are equal.

∠A = ∠D , ∠B = ∠E and ∠C = ∠F

properties of congruent triangles

Congruence Test

Here are 4 important congruence tests.

1. Side ‒ Side ‒ Side

congruence test sss

∠A = ∠D       AB = DE

∠B = ∠E        BC = EF

∠C = ∠F        AC = DF

∆ABC coincide with ∆DEF

So ∆ABC ≅ ∆DEF (SSS Rule)

 

2. Angle ‒ Side ‒ Angle

congruence test ASA

Let BC = EF, ∠B = ∠E, AB = DE, ∠C = ∠F

So ∆ABC ≅ ∆DEF (ASA Rule)

 

3. Side ‒ Angle ‒ Side

congruence test SAS

AB = EF

∠ABC = ∠EFG

BC = FG

So ∆ABC ≅ ∆EFG (SAS Rule)

Note: The angle must be in between the 2 sides.

 

4. Right angled ‒ Hypotenuse ‒ Side

congruence test RHS

∠B = ∠Y = 90°

AB = XY

AC = XZ

So ∆ABC ≅ ∆XYZ (SAS Rule)

Congruent Triangles Examples

congruent triangles SSS

In ∆ABC and ∆ABD,

BC = AD

AC = BD

AB is common

∴ ∆ABC ≡ ∆ABD (SSS)

congruent triangles AAS

In ∆ABE and ∆FCE,

AB = FC

∠BAE = ∠CFE

∠AEB = ∠FEC (vertically opposite angles)

∴ ∆ABE ≡ ∆FCE (AAS)

congruent triangles SAS

In ∆ABC and ∆DEF,

AB = DE

BC = EF

∠ABC = ∠DEF

∴ ∆ABC ≡ ∆DEF (SAS)

congruent triangles RHS

In ∆ABC and ∆DCE,

∠ACB = ∠ DCE = 90°

AB = DE (Hypotenuse)

AC = DC

∴ ∆ABC ≡ ∆DCE (RHS)

 

Last Minute Revision for O Level Math?

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Secondary Math Revision Notes

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congruence test notes

 

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