How to use the AA similarity to show that the given triangles are similar: postulate, 1 example, and its solution.
For two triangles,
if two angles of each triangle are congruent,
then those two triangles are similar.
This is the AA similarity postulate.
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
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.