Unit 4.9Similarity in Triangles

SimilarDefinition:  In mathematics, polygons are

similar if their corresponding (matching) angles are congruent (equal in measure) and the ratio of their corresponding sides are in proportion.

Similar is represented by a ~

Jim

DaveMeet Jim and Dave.

Jim ~ Dave

Jim

Dave

What is the ratio of Jim’s height to Dave’s height?5:10 which is 1:2

Jim

Dave

What is the ratio of Jim’s width to Dave’s width?2:4 which is 1:2

Note: the ratio is the same for both height and width!

Jim

Dave

Therefore, the scale factor of Jim to Dave is 1:2

We can write Jim and Dave’s dimensions as proportions:

24

= 510

Similar Triangles:

How do you know if two triangles are similar?Just like with congruent triangles, we have a

postulate and theorems to prove triangles are similar. They are:Angle-Angle Similarity Postulate (AA~)Side-Angle-Side Theorem (SAS~)Side-Side-Side Theorem (SSS~)

How do you know if two triangles are similar?http://www.mathopenref.com/similartriangles.html

Angle-Angle Similarity Postulate (AA~)If two angles of one triangle are

congruent to two angles of another triangle, then the triangles are similar.

Angle-Angle Similarity Postulate (AA~)More Examples:

Angle-Angle Similarity Postulate (AA~)More Examples:

Side-Angle-Side Similarity Theorem (SAS~)If an angle of one triangle is congruent to an

angle of a second triangle and the sides including the angle are proportional, then the triangles are similar.

Side-Side-Side Similarity Theorem (SAS~)If the corresponding sides of two triangles are

proportional, then the triangles are similar.