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Prove theorems about triangles

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Presentation on theme: "Prove theorems about triangles"— Presentation transcript:

1 Prove theorems about triangles
MACC.912.G-SRT.2.4 Prove theorems about triangles

2 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

3 The Sunshine Skyway Bridge

4 Find at least three triangles.
Are the triangles similar? Explain

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

6 Are the road deck and the concrete tower parallel or perpendicular?
Would the road deck be parallel or perpendicular to the ocean waves?

7 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?

8 Another View… Parallel lines? Perpendicular Lines? Similar Triangles?

9 A Tale of Two Bridges

10 Assessment Example 1: What is the value of x in the diagram? M 12 9
x 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.

11 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

12 Assessment Example 1: What is the value of x in the diagram? M
PK = NL Side-Splitter Theorem KM LM x+1 K L x x+1 = x Substitution P N 9(x+1) = 12x Cross-Product Property 9x + 9 = 12x Distributive Property 9 = 3x Subtract 9x from each side. x = Divide each side by 3.

13 Assessment Your Turn: What is the value of “a” in the diagram? a 12

14 Assessment Your Turn: What is the value of “a” in the diagram? a 12
a+4 = Side-Splitter Theorem a a 18a = 12(a+4) Cross-Product Property 18a = 12a Distributive Property 6a = Subtract 12a from both sides. a = Divide each side by 6.

15 Independent Practice/Homework
Practice and Problem-Solving Exercises Prentice Hall , page 500: 1-15 all

16 Background Knowledge Review Terminology Triangle similarity Parallel
Perpendicular Corresponding Angles

17 Hook/Motivation for Lesson (More time here)
Bridge-building Video Worksheet / Anticipation Guide

18 Discovery Learning Technique (More time here)
Worksheet/Hands-On Activity Students Make and Test Conjectures

19 Multiple Representations
Small Triangle / Graph Paper Picture of Bridge Angles/Proportional/Slope (?)

20 Questions: How do you determine the length of the yellow tubes that contain cables Are 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

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