# ASA Congruence (Angle-Side-Angle Congruence)

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

## Postulate

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

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 *AC* ≅ *AC*.

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*.