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.