# SAS Similarity

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

## Postulate

For two triangles,

if two sides of each triangle are proportional

(a/a' = b/b'),

and if the inscribed angles of each triangle

are congruent,

then those two triangles are similar.

This is the SAS similarity postulate.

(Side-Angle-Side similarity)

## Example

Draw △APQ.

Draw △ACB.

Make the shape of △ACB

the same as △APQ.

Use these two triangles

to show that △APQ and △ACB are similar.

∠A in the left triangle

and ∠A in the right triangle

are the same.

So ∠A ≅ ∠A.

Find the ratios of the corresponding sides.

3/6 = 1/2

4/8 = 1/2

3/6 = 1/2

4/8 = 1/2

So 3/6 = 4/8 = 1/2.

Two sides of each triangle are proportional:

3/6 = 4/8.

And the inscribed angles of each triangle

are congruent:

∠A ≅ ∠A.

Then, by the SAS similarity postulate,

△APQ and △ACB are similar.

This is the proof of the example.