Chapter 7 Similarity. Definition: Ratio The angles of a pentagon are in ratio 4:2:5:5:2, find the measure of each angle 4x+2x+5x+5x+2x = 540 18x.

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Presentation transcript:

Chapter 7 Similarity

Definition: Ratio

The angles of a pentagon are in ratio 4:2:5:5:2, find the measure of each angle 4x+2x+5x+5x+2x = x = 540 x = , 60, 150, 150, 60

Definition: Proportion

Identify the means and extremes:

Definition: Geometric Mean A proportion in which the second and third terms are equal

Find the geometric mean between 5 and 28.

18 is the geometric mean between 7 and what number?

Properties of Proportions:

Definition: Similar Polygons Two polygons are similar iff, 1)Corresponding angles are congruent 2)Corresponding sides are in proportion

If ABCDE ~ NGPHM, then….

Ways to prove triangles similar: 1) AA~ theorem 2) SSS~ theorem 3) SAS~ theorem

AA~ theorem If two angles of one triangle are congruent to corresponding angles of another triangle, then the triangles are similar.

Find BE

How tall is the tree?

Given: BC // DE Prove: ∆ABC ~ ∆ADE

Triangle Proportionality Thm aka (side splitter thm)

Triangle Angle Bisector Thm