# AA Similarity

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

## Postulate

### Postulate

For two triangles,

if two angles of each triangle are congruent,

then those two triangles are similar.

This is the AA similarity postulate.

(Angle-Angle similarity)

## Example

### Example

### Solution

To write a two-column proof,

make a two-column form like this.

Start from the given statement:

AB // CD.

[ // ] means [is parallel to].

∠PAB and ∠PDC are

alternate interior angles in parallel lines.

Alternate interior angles in parallel lines

are congruent.

So ∠PAB ≅ ∠PDC.

∠APB and ∠DPC are vertical angles.

Vertical angles are congruent.

So ∠APB ≅ ∠DPC.

For △PAB and △PDC,

two angles of each triangle are congruent.

∠PAB ≅ ∠PDC

∠APB ≅ ∠DPC

Then, by the AA similarity postulate,

△PAB and △PDC are congruent.

You found the Prove statement

△PAB ~ △PDC.

So close the two-column form

by drawing the bottom line.

This is the proof of the example.