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.

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).  

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

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

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

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

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

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

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

Lesson 5: Using Proportional Segments  

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?  

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