# 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.

**Before you read on, you might want to download this entire revision notes in PDF format to print it out, or to read it later. **

**This will be delivered to your email inbox.**

## 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 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

## Congruence Test

Here are 4 important congruence tests.

1. Side ‒ Side ‒ Side

∠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

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

So ∆ABC ≅ ∆DEF (ASA Rule)

3. Side ‒ Angle ‒ Side

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

∠B = ∠Y = 90°

AB = XY

AC = XZ

So ∆ABC ≅ ∆XYZ (SAS Rule)

## Congruent Triangles Examples

In ∆ABC and ∆ABD,

BC = AD

AC = BD

AB is common

∴ ∆ABC ≡ ∆ABD (SSS)

In ∆ABE and ∆FCE,

AB = FC

∠BAE = ∠CFE

∠AEB = ∠FEC (vertically opposite angles)

∴ ∆ABE ≡ ∆FCE (AAS)

In ∆ABC and ∆DEF,

AB = DE

BC = EF

∠ABC = ∠DEF

∴ ∆ABC ≡ ∆DEF (SAS)

In ∆ABC and ∆DCE,

∠ACB = ∠ DCE = 90°

AB = DE (Hypotenuse)

AC = DC

∴ ∆ABC ≡ ∆DCE (RHS)

## Last Minute Revision for O Level Math?

## Check out our exam guide on other topics here!

**Before you go, you might want to download this entire revision notes in PDF format to print it out, or to read it later. **

**This will be delivered to your email inbox.**

**Does your child need help in his or her studies?**

**1) Live Zoom Lessons at Grade Solution Learning Centre**

At Grade Solution Learning Centre, we are a team of dedicated educators whose mission is to guide your child to academic success. Here are the services we provide:

– Live Zoom lessons

– EdaptIQ™, a smart learning platform that tracks your child’s progress, strengths and weaknesses through personalised digital worksheets.

– 24/7 Homework Helper Service

We provide all these services above at a very affordable monthly fee to allow as many students as possible to access such learning opportunities.

We specialise in English, Math, and Science subjects.

You can see our fees and schedules here >>

**2) Pre-recorded Online courses on Jimmymaths.com**

If you are looking for something that fits your budget, or prefer your child learn at his or her own pace, you can join our pre-recorded online Math courses.

Your child can:

– Learn from recorded videos

– Get access to lots of common exam questions to ensure sufficient practice

– Get unlimited support and homework help

You can see the available courses here >>