ASA Congruence (Angle-Side-Angle Congruence)

ASA Congruence (Angle-Side-Angle Congruence)

How to solve ASA congruence problems: postulate, example and its solution (proof)."

Postulate

ASA Congruence: If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then those two triangles are congruent.

If two angles and the included side of a triangle
are congruent to
two angles and the included side of another triangle,
then those two triangles are congruent.

Example

Given: line segment AC bisects angle BAD and angle BCD. Prove: triangle ABC is congruent to triangle ADC.

Start from the given statement.

Two column proof

AC bisects ∠BAD.
So m∠BAC ≅ m∠DAC.

AC bisects ∠BCD. (purple angles)
So m∠BCA ≅ m∠DCA. (red angles)

AC is equal to itself.
So ACAC.

Two angles and the included side of △ABC
are congruent to
two angles and the included side of △ADC.

Then, by the ASA congruence postulate,
ABC ≅ △ADC.