SSS Similarity

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

Postulate

Postulate

For two triangles,
if three sides of each triangle are proportional
(a/a' = b/b' = c/c'),
then those two triangles are similar.

This is the SSS similarity postulate.
(Side-Side-Side similarity)

Example

Example

Solution

Draw △ABD.

Draw △DCB.

Make the shape of △DCB
the same as △ABD.

Use these two triangles
to show that △ABD and △DCB are similar.

Find the ratios of each corresponding sides.

6/3 = 2

4/2 = 2

8/4 = 2

6/3 = 2
4/2 = 2
8/4 = 2

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

Three sides of each triangle are proportional:
6/3 = 4/2 = 8/4.

Then, by the SSS similarity postulate,
△ABD and △DCB are similar.

This is the proof of the example.