1. 9.4(a) Notes: | | Lines and Propor­tion­a­l Parts
Date:
9.4(a) Notes: | | Lines and Propor­tion­a­l Parts
Lesson Objective: Use proportional parts within triangles and with parallel lines.
CCSS: G.SRT.4, 5 
You will need: colored pens 
Real-World App: What is the length of the ocean frontage?
This is Jeopardy!:  This is the length of the hypotenuse of a right triangle with legs 9 and 12.

2. Lesson 1: Triangle Propor­tion­a­li­ty Theorem
Plot ∆ACD with vertices A(0, 9), C(0, 0), and D(12, 0). Plot ∆ABE with vertices A(0, 9), B(0, 6), and E(4, 6).

3. Lesson 1: Triangle Propor­tion­a­li­ty Theorem
Are ∆ABE and ∆ACD similar? By what postulate or theorem?
Statements
Reasons 1. 2. 3.

4. Lesson 1: Triangle Propor­tion­a­li­ty Theorem
Find and label the lengths of AB, AE, BC and ED.
AB = __ BC
AE = __ ED

5. Lesson 1: Triangle Propor­tion­a­li­ty Theorem
AB = __ BC
AE = __ ED
Triangle Proportionality Theorem:
If BE | | CD, then AB = AE .
BC ED

6. Lesson 1: Triangle Propor­tion­a­li­ty Theorem
AB = __ BC
AE = __ ED
Converse Δ Proportionality Theorem:
If AB = AE , then BE | | CD.
BC ED

7. Lesson 2: Finding the Length of a Side
QR and TS are | |. If PS = 12.5, SR = 5 and PT = 15, find TQ.
  Q T
P S R

8. Lesson 3: Determining if Lines are | |
If PS = 16, SR = 4 and TQ is one-fourth the length of PT, is TS | | QR?
  Q T
P S R

9. Lesson 4: Proportional Parts of | | Lines
Proportional Parts of | | Lines:

10. Lesson 5: Using Proportional Segments

11. 9.4(a): Do I Get It? Yes or No 1.
In ΔPQR, SR = 3, PS = 9 and TQ is one-third the length of PT. Is ST | | RQ?

12. 9.4(a): Do I Get It? Yes or No 3.