Download Angle-Angle (AA) Similarity

Geometry Pre-AP
Section 7.3 and 7.4
Notes
TRIANGLE SIMILARITY
What were the abbreviations for the “shortcuts” we can use to prove triangles CONGRUENT?
_____________ , ____________ , ______________ , ______________
Likewise, there are several ways/ “shortcuts” to prove that triangles are SIMILAR.
Angle-Angle (AA) Similarity
Example:
Side-Side-Side (SSS) Similarity
Example:
Side-Angle-Side (SAS) Similarity:
Example:
Verify that the triangles are similar and EXPLAIN why.
1. PQR and PRS
Example:
REMEMBER: For triangles to be similar
1). All angles must be congruent
2). All sides must be proportional!
2. JKL and JMN
3. Explain why RSV ~ RTU
4. Given  ABC~  XYZ, m  A = 50°, m  X = (2x + 5y)°, m  Z = (5x + y)°, and that m  B = (102 – x)°, find m  Z.
APPLYING THE PROPERTIES OF SIMILAR TRIANGLES:
Triangle Proportionality Theorem
Example:
Finding the length of a segment:
Example 1.
Find CY
Converse of the Triangle Proportionality Theorem
Example:
Example 2.
Show that MN ║ KL
Two-Transversal Proportionality Theorem
Example 3. An artist used perspective to draw guidelines to help her sketch a row of parallel trees. She then
checked the drawing by measuring the distances between the trees. What is LN?
Triangle Angle Bisector Theorem
What does this mean?
Example 4.
Find RV and VT.
Example 5.
The perimeter of  ABC is 128 miles. Find AX and AY.