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
