Congruent triangles have exactly the same shape and size. Properties of congruent triangles are: • e

Question

Congruent triangles have exactly the same shape and size.
Properties of congruent triangles are:
• equal corresponding angles
• equal corresponding sides
The symbol for congruency is ‘$\equiv $’.

Congruency Tests for Triangles

SSS Congruency Test

$AB=XY$,

$BC=YZ$,

$AC=XZ$.

\[\therefore \Delta ABC \equiv \Delta XYZ\]

($\text{SSS}$ Congruency Test)

SAS Congruency Test

$AB=XZ$,

$BC=ZY$,

$\angle ABC=\angle XZY$ (Included Angle)

\[\therefore \Delta ABC \equiv \Delta XZY\]

($\text{SAS}$ Congruency Test)

AAS Congruency Test

$PQ=YX$,

$\angle PQR=\angle YXZ$,

$\angle PRQ=\angle YZX$,

\[\therefore \Delta PQR \equiv \Delta YXZ\]

($\text{AAS}$ Congruency Test)

RHS Congruency Test

$AC=DE$,

$AB=DF$,

$\angle ABC=\angle DFE=90^\circ$

\[\therefore \Delta ABC \equiv \Delta DFE\]

($\text{RHS}$ Congruency Test)

The most important things that you have to take notes when proving a pair of congruent triangles:
• To list down the $3$ equivalent corresponding angles or corresponding sides and give reasons or justifications necessary.
• Never make assumptions if questions did not state so.
• To write down the test property ($\text{SSS}$, $\text{SAS}$, $\text{AAS}$ or $\text{RHS}$).
• Order of naming a pair of congruent triangles is important.

Accepted Answer

$\text{SSS},\ \text{SAS},\ \text{AAS},\ \text{RHS}$

Congruency Tests