Download Title : Cases of congruent triangles Objective : In this

Title : Cases of congruent triangles
Objective : In this lesson we will learn about the different cases of congruencies in
triangles.
In geometry, two figures or objects are congruent if they have the same shape and size.
Two triangles are congruent if they have exactly the same three sides and same three
angles.
But we don't have to know all three sides and all three angles ,usually three out of the
six is enough.
There are five ways to find if two triangles are congruent:
SSS, SAS, ASA, AAS and HL.
Congruence between two triangles can be shown through the following comparisons:

SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and
the included angles are equal in measurement, then the triangles are congruent.

SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length,
then the triangles are congruent.
ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in
measurement, and the included sides are equal in length, then the triangles are
congruent.
AAS (Angle-Angle-Side): If two pairs of angles of two triangles are equal in
measurement, and a pair of corresponding non-included sides are equal in length,
then the triangles are congruent.


RHS (Right-angle-Hypotenuse-Side): If two right-angled triangles have their
hypotenuses equal in length, and a pair of shorter sides are equal in length, then the
triangles are congruent. Also known as HL (Hypotenuse-Leg).
Caution ! we don't use "AAA"
AAA means we are given all three angles of a triangle, but no sides.
This is not enough information to decide if two triangles are congruent!
Because the triangles can have the same angles but can be of different sizes.
Summary: In this lesson we have learned about SSS, SAS, ASA, AAS and HL
congruencies to find if two triangles are congruent.