ASA Congruence

How to use the ASA congruence to show that the given triangles are similar: postulate, 1 example, and its solution.

Postulate

Postulate

For two triangles,
if two angles and the included side of each triangle
are congruent,
then those two triangles are congruent.

This is the ASA congruence postulate.
(Angle-Side-Angle congruence)

Example

Example

Solution

To write a two-column proof,
make a two-column form like this.

Start from the given statement:
AC bisects ∠BAD and ∠BCD.

AC bisects ∠BAD.

Then, by the definition of an angle bisector,
∠BAC ≅ ∠DAC.

AC also bisects ∠BCD.

Then, by the definition of an angle bisector,
∠BCA ≅ ∠DCA.

AC is congruent to itself:
ACAC.

This is the reflexive property.

For △ABC and △ADC,
two angles and and the included side of each triangle
are congruent.

∠BAC ≅ ∠DAC
∠BCA ≅ ∠DCA
ACAC

Then, by the ASA congruence postulate,
△ABC and △ADC are congruent.

You found the Prove statement
△ABC ≅ △ADC.

So close the two-column form
by drawing the bottom line.

This is the proof of the example.