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Congruent Triangles

See how to prove that the given triangles are congruent.
5 examples and their solutions.

SSS Congruence

Postulate

For two triangles,
if 3 sides of each triangle are congruent
(Side-Side-Side),
then those two triangles are congruent.

Example

Given: ABAD
C is the midpoint of BD.
Prove: △ABC ≌ △ADC

Solution

SAS Congruence

Postulate

For two triangles,
if 2 sides & 1 angle of each triangle are congruent
(Side-Angle-Side),
then those two triangles are congruent.

Example

Given: P is the midpoint of AD and BC.
Prove: △ABP ≌ △DCP

Solution

ASA Congruence

Postulate

For two triangles,
if 1 side & 2 angles of each triangle are congruent
(Angle-Side-Angle),
then those two triangles are congruent.

Example

Given: AC bisects ∠BAD and ∠BCD.
Prove: △ABC ≌ △ADC

Solution

AAS Congruence

Theorem

For two triangles,
if 2 angles & non-included side of each triangle are congruent
(Angle-Angle-Side),
then those two triangles are congruent.

Example

Given: ABCD
∠PAB ≌ ∠PCD.
Prove: △PAB ≌ △PCD

Solution

HL Congruence

Postulate

For two right triangles,
if a hypotenuse and a leg of each triangle are congruent,
then those two right triangles are congruent.

Example

Given: ∠A and ∠D are right angles.
ABCD
Prove: △ABC ≌ △DCB

Solution