# 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:

AC ≅ AC.

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

AC ≅ AC

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.