Similarity in Triangles. Similar Definition: In mathematics, polygons are similar if their corresponding (matching) angles are congruent (equal in measure)

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Presentation transcript:

Similarity in Triangles

Similar Definition: 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 ~

5:10 which is 1:2

2:4 which is 1:2 Note: the ratio is the same for both height and width!

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

We can write Jim and Dave’s dimensions as proportions: 2 4 = 5 10

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?

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.