Section 8-3 Advanced Triangles SPI 31A: identify corresponding parts of similar and congruent geometric figures

Objectives:• Use and apply AA, SAS, and SSS similarity statements

3 Methods to Determine if Triangles are Similar

1. Angle-Angle (AA~) Similarity Postulate2. Side-Side-Side (SSS~) Similarity Thm3. Side-Angle-Side (SAS~) Similarity Thm

Angle-Angle (AA~) Similarity Thm

AA~ Similarity Postulate

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

Using (AA~) Similarity Theorem

Explain why the triangles are similar and write a similarity statement.

R V Given (measures are equal)RSW VSB Vertical s∆RSW ~ ∆VSB AA~ Postulate

Side-Angle-Side (SAS~) Similarity Thm

SAS~ Similarity Theorem

If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.

ABC EBD Vertical angles

AB = 12 = 2 EB 18 3

CB = 16 = 2DB 24 3

Proportional

∆ABC ~ ∆EBD by SAS ~

Side-Side-Side (SSS~) Similarity Thm

SSS~ Similarity Theorem

If the corresponding sides of two triangles are proportional, then the triangles are ~.

Indirect Measurement using Similarity

Explain why the triangles are ~, then find the distance represented by x.

AA~ Postulate; 220 yards

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