SAS Similarity

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

Postulate

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

Example

Solution

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.