Prove theorems about triangles

Today, we will learn How a line parallel to one side of a triangle

divides the other two sides proportionally, and conversely, using various methods including

1) Pythagorean Theorem

2) Side-Splitter Theorem

3) Slope

http://www.youtube.com/watch?v=WrfTS64WpTw The Sunshine Skyway Bridge

Find at least three triangles.

Are the triangles similar? Explain

Where are the parallel lines? Where are the similar triangles?

Are the road deck and the concrete tower parallel or perpendicular?

Would the road deck be parallel or perpendicular to the ocean waves?

How do you determine the length of the yellow tubes that contain cables? What formula would you use?

Are the Yellow tubes containing cables parallel or not?

Another View…

Parallel lines? Perpendicular Lines? Similar Triangles?

A Tale of Two Bridges

AssessmentExample 1: What is the value of x in the diagram?

M 12

9

x+1 K L x

P N

Plan: How can you use the parallel lines in the diagram?

Use the Side-Splitter Theorem to set up a proportion.

Side-Splitter Theorem:If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

If . . . Then . . . RS || XY XR = YS RQ SQ Q

R S

X Y

AssessmentExample 1: What is the value of x in the diagram?

M PK = NL Side-Splitter Theorem 12

9 KM LM x+1 K

L x

x+1 = x Substitution P N

12 9 9(x+1) = 12x Cross-Product Property

9x + 9 = 12x Distributive Property

9 = 3x Subtract 9x from each side.

x = 3 Divide each side by 3.

AssessmentYour Turn: What is the value of “a” in the

diagram?

a 12

a+4 18

AssessmentYour Turn: What is the value of “a” in the diagram? a

12 a+4 = 18 Side-Splitter Theorem

a 12 a+4

18

18a = 12(a+4) Cross-Product Property

18a = 12a + 48 Distributive Property

6a = 48 Subtract 12a from both sides.

a = 8 Divide each side by 6.

Practice and Problem-Solving ExercisesPrentice Hall , page 500: 1-15 all

Background Knowledge

Review Terminology

Triangle similarity

Parallel

Perpendicular

Corresponding Angles

Hook/Motivation for Lesson (More time here)

Bridge-building Video

Worksheet / Anticipation Guide

Discovery Learning Technique (More time here)

Worksheet/Hands-On Activity

Students Make and Test Conjectures

Multiple RepresentationsSmall Triangle / Graph Paper

Picture of Bridge

Angles/Proportional/Slope (?)

Questions:How do you determine the length of the yellow tubes that contain cablesAre the road deck and the concrete tower parallel or perpendicular?Are the Yellow tubes containing cables parallel or not?Would the road deck be parallel or perpendicular to the ocean waves?What formula could you use to determine the length of the yellow cables?Find at least three triangles Are the triangles simular? Explain