1. We will determine1 how to apply Triangle Proportionality2 theorem to find segment lengths.
LEARNING OBJECTIVE
Definition
figure out
Two ratios that have the same value.
Declare the Objective
A: Read the Objective to B.
B: Define Proportionality to A
CFU
What are we going to learn today? What is “Proportionality” mean?
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

2. ACTIVATE PRIOR KNOWLEDGE
Remember the Concept
Cross Products property.
Solve for x use the Cross products property.
1. Solve for x,
2. Solve for x,
= ? 4 x 8 3
x –
Cross products property
Cross products property
4(x – 3) = x 8
𝟓𝟒 𝟒𝒙+𝟒 =𝟒𝟖(𝟓𝒙+𝟏)
Simplify.
216𝒙 + 216=𝟐𝟒𝟎𝒙+𝟒𝟖
4x – 12 = 8x
−𝟐𝟒𝟎x
−𝟐𝟏𝟔
−𝟐𝟒𝟎x
−𝟐𝟏𝟔
ACTIVATE PRIOR KNOWLEDGE
Subtract 4x from each side.
−𝟐𝟒𝒙=−𝟏𝟔𝟖
–12 = 4x
𝒙=𝟕
Divide each side by 4.
–3 = x
Make the Connection
Students, you already know how to use cross product to solve for x. Today, we will learn how to apply Triangle Proportionality theorem to find segment lengths.

3. B Explain to A: what is Triangle Proportionality theorem states?
On your white board, using the Triangle Proportionality Theorem write the correct ratios?
CFU T
B Explain to A: what is Triangle Proportionality theorem states?

4. 𝟓𝒙+𝟓 𝟒 = 𝟖𝒙+𝟏 𝟓 Check for Understanding
How did I/you write the proportional ratios?
How did I/you I solve for x?
CFU 1 2
Write the ratio using Triangle Proportionality theorem.
Use the Cross Product rule to solve for x.
Check you answer.
Steps to find the segment lengths 1 2 3 1. 2.
Check for Understanding
A Explain to B: How did I write the ratio and find the x?
CONCEPT DEVELOPMENT
𝟓𝒙+𝟓 𝟒 = 𝟖𝒙+𝟏 𝟓
Cross products property
Cross products property
𝟓𝟒 𝟒𝒙+𝟒 =𝟒𝟖(𝟓𝒙+𝟏)
𝟓 𝟓𝒙+𝟓 =𝟒(𝟖𝒙+𝟏)
216𝒙 + 216=𝟐𝟒𝟎𝒙+𝟒𝟖
−𝟐𝟒𝟎x
−𝟐𝟏𝟔
−𝟐𝟒𝟎x
−𝟐𝟏𝟔
𝟐𝟓𝒙+𝟐𝟓 =𝟑𝟐𝒙+𝟒
−𝟐𝟓
−𝟐𝟒𝒙=−𝟏𝟔𝟖
−𝟑𝟐𝒙
−𝟐𝟓
−𝟑𝟐𝒙
𝒙=𝟕
−𝟕𝒙=−𝟐𝟏
𝒙=𝟑

5. no Check for Understanding
How did I/you write the proportional ratios?
How did I/you I solve for x?
CFU 1 2
Write the ratio using Triangle Proportionality theorem.
Use the Cross Product rule to solve for x.
Check you answer.
Steps to find the segment lengths 1 2 3 1. 2.
In order to show that we must show that
CONCEPT DEVELOPMENT
Since
the sides are proportional.
Check for Understanding
B Explain to A: How did I show that GH is parallel to FE? no
Answer: Since the segments have
proportional lengths, GH || FE.

6. Relevance Reason #1: Proportionality is used Maps
In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find x.
Notice that the streets form a triangle that is cut by parallel lines. So you can use the Triangle Proportionality Theorem.
Relevance Reason #1: Know how to find geometric mean will help you do well on tests (PSAT, SAT, ACT, GRE, GMAT, LSAT, etc..).
Check for Understanding
Does anyone else have another reason why it is relevant to use verb tense correctly?
Which reason is most relevant to you? Why?
Answer: x = 32

7. What did you learn today about how to apply Triangle Proportionality theorem to find segment lengths.
Word Bank
Proportionality
Segment Lengths
SUMMARY CLOSURE
Today, I learned how to __________________
______________________________________________________________.