1. Identify similar triangles Use similar triangles to solve problems
Eiffel Tower

2. POSTULATE
Angle-Angle (AA) Similarity
If the two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Example:

3. Side-Side-Side (SSS) Similarity
THEOREM
Side-Side-Side (SSS) Similarity
If the measures of the corresponding sides of two triangles are proportional, then the triangles are similar.
Example: S Q a ax b bx c P R T cx U

4. Side-Angle-Side (SAS) Similarity
THEOREM
Side-Angle-Side (SAS) Similarity
If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. S Q
Example: a ax b bx P R T U

5. Example 1 – Determine Whether Triangles are Similar
In the figure, , BE = 15, CF = 20, AE = 9, and DF = 12. Determine which triangles in the figure are similar. C B G A F E D

6. Example 1 – Determine Whether Triangles are Similar
In the figure, , BE = 15, CF = 20, AE = 9, and DF = 12. Determine which triangles in the figure are similar. C
Solution:
Triangle FGE is an isosceles triangle, so B G A F E D

7. Example 1 – Determine Whether Triangles are Similar
In the figure, , BE = 15, CF = 20, AE = 9, and DF = 12. Determine which triangles in the figure are similar. C
If the measures of the corresponding sides that include the angles are proportional, then the triangles are similar. B G A F E D
By SAS similarity, ∆ABE ~ ∆DCF

8. THEOREM
Similarity of triangles is reflexive, symmetric, and transitive.
Examples:
Reflexive: ∆ABC ~ ∆ABC
Symmetric: If ∆ABC ~ ∆DEF, then ∆DEF ~ ∆ABC
Transitive: If ∆ABC ~ ∆DEF and ∆DEF ~ ∆GHI, then ∆ABC ~ ∆GHI

9. Example 2 – Parts of Similar Triangles
Algebra: Find AE and DE C 5 A
X - 1 E 2
X + 5 D B