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.