Chapter 5 ratios rates proportions section 5
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Chapter 5 : Ratios, Rates & Proportions Section 5. Using Similar Figures. Anticipatory Set . Buffaloes, I need some help.

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Chapter 5 : Ratios, Rates & Proportions Section 5

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Chapter 5 ratios rates proportions section 5

Chapter 5: Ratios, Rates & Proportions Section 5

Using Similar Figures


Anticipatory set

Anticipatory Set

  • Buffaloes, I need some help.

  • Look at the tiles in my kitchen. They are huge. I have a brilliant idea, lets remodel! However, I will only remodel with your help. I still want tile in my kitchen, but I want smaller pieces of tile. You’re my construction team! Let’s do this!


California standards

California Standards

  • Number Sense 1.3: Use proportions to solve problems. Use Cross-Multiplication as a method for solving such problems.


Key vocabulary language of the discipline

Key VocabularyLanguage of the Discipline

  • PROPORTION: An equation stating that two RATIOS are EQUAL.

    • Examples: 1/2 =2/4a/b = c/d, where b and d CANNOT equal ZERO

  • POLYGONS: A closed plane figure formed by three or more line segments that DO NOT cross

  • SIMILAR POLYGONS: A geometric occurrence where two polygons have corresponding angles that possess the same measure AND the lengths of the corresponding sides form equivalent ratios.

  • CROSS PRODUCTS PROPERTY: When given two ratios, this property states that the CROSS PRODUCTS will EQUAL each other. If the two ratios have EQUAL cross products, they form a PROPORTION.

  • INDIRECT MEASUREMENT: Examining Similar Polygons by using proportions to determine missing measures.


What is a proportion

What is a PROPORTION?

  • PROPORTION:

    • A PROPORTION is an EQUATION stating that 2 RATIOS are EQUAL.

    • Another way to test for PROPORTIONALITY is to use the Cross Products Property.

      • Here, 2 ratios are set equal, values are multiplied diagonally, if BOTH resulting products are EQUAL you have a PROPORTION.

      • If not EQUAL, the ratios are NOT PROPORTIONAL.


Cross products property

CROSS PRODUCTS PROPERTY

  • a Mathematic Property will come in handy because that give the RULE or GUIDELINE on how to attack a problem.

  • The CROSS PRODUCTS PROPERTY states that if two ratios form a proportion, the CROSS PRODUCTS are EQUAL. If two ratios have EQUAL Cross Products, they form a PROPORTION.

  • There are two ways to look at PROPROTIONS.

    • ARITHMETIC: 5/7 = 25/35

      (5)(35) = (7)(25)

      175 = 175

    • ALGEBRAIC: a/b = c/db and d CANNOT equal ZERO (0).

      ad = bc


Finding a missing measure example 1

Finding A Missing Measure: Example 1

  • Two Triangles exist and are similar. Find the value of T.

    • The small triangle has two sides with a measure of 22 and 24 inches.

    • The large triangle has similar sides of T and 36 inches.

  • Highlight the side with both numbers with a yellow highlighter

  • Highlight the side with the variable with a green highlighter.

  • Using Proportions, we have:

    • 22/24 = T/36

    • (22)(36) = (24)(T)

    • 33 = T

37 inches

22 inches

24 inches

55.5 inches

T

36 inches


Finding a missing measure example 2

Finding A Missing Measure: Example 2

  • +Two Parallelograms exist and are similar. Find the value of P.

    • ++The small parallelogram has two pairs of sides with measures of 13 and 19 cm

    • +The large parallelogram has similar sides of P and 57 cm.

    • Highlight the side with both numbers with a yellow highlighter

    • Highlight the side with the variable with a green highlighter.

  • +Using Proportions, we have:

    • +13/19 = P/57

    • +(13)(57) = (19)(P)

    • +39 = P

13 cm

19 cm

P

57 cm


Finding a missing measure example 3

Finding A Missing Measure: Example 3

34 inches

  • Two Trapezoids exist and are similar. Find the value of T.

    • The small trapezoid has two sides with a measure of 50, one side of 34 and one of 44 inches.

    • The large trapezoid has similar sides where one is T inches, two are 80 inches and the other is 70.4.

  • Highlight the side with both numbers with a yellow highlighter

  • Highlight the side with the variable with a green highlighter.

  • Using Proportions, we have:

    • 34/50 = T/80

    • (34)(80) = (50)(T)

    • 54.4 = T

50 inches

44 inches

T

80 inches

70.4 inches


Quick review

Quick Review

  • PROPORTIONS

    • A pair of ratios that equal one another.

    • Proportions can be solved using multiple methods.

  • SIMLIAR FIGURES

    • Similar Figures assumes that if two polygons are similar, a proportion can be formed between the two and you can solve using Cross Products Property.

    • Hint: Analyze your geometric shape carefully, make certain that it is similar and labeled correctly to set proportions.

  • Using CROSS PRODUCTS PROPERTY to Solve

    • Cross Products Property states that a pair of Ratios are a PROPORTION when their cross products equal the same value.

    • Remember that you are taking the NUMERATOR from one Ratio and MUTLIPLYING it by the DENOMINATOR of the other.

    • Use this property and ALGEBRA to solve the missing value.

    • Once the missing cross product is determined, DOUBLE CHECK to make certain it works in the original proportion.


Check for understanding

Check for Understanding

  • Please determine the BEST answer for the following expression.

  • Carry out ALL work and calculations in your NOTES for later reference

  • Please write your answer on your white boards and wait for the teacher’s signal.

  • On the count of 3, hold up your wipe boards.


C4u question 1 checking for understanding

C4U Question #1Checking for Understanding

  • Question #1:

    -The 2 Triangles are Similar.

    -What Proportion can be used to find the Missing Measure?

    Select the BEST answer:

    A. 12/16 = Y/16

    B. Y/16 = 60/48

    C. 48/36 = Y/16

    D. 36/12 = 16/Y

Y

12 cm

16 cm

60 cm

36 cm

48 cm


C4u question 2 checking for understanding

C4U Question #2Checking for Understanding

  • Question #2:

    -The 2 Triangles are Similar.

    -What Proportion can be used to find the Missing Measure?

    Select the BEST answer:

    A. 25/E = E/60

    B. 5/E = 60/25

    C. E/25 = 5/60

    D. E/5 = 60/25

5 cm

E

25 cm

60 cm

48 cm


C4u question 3 checking for understanding

C4U Question #3Checking for Understanding

  • Question #3:

    -The 2 Triangles are Similar.

    -What is the value of the Missing Measure?

    Select the BEST answer:

    A. R = 18.4 cm

    B. R = 20.0 cm

    C. R = 22.6 cm

    D. R = 19.7 cm

R

14 cm

11 cm

60 cm

42 cm

33 cm


C4u question 4 checking for understanding

C4U Question #4Checking for Understanding

  • Question #4:

    -The 2 Parallelograms are Similar.

    -What is the value of the Missing Measure?

    Select the BEST answer:

    A. Y = 38.8

    B. Y = 40.6

    C. Y = 39.8

    D. Y = 41.4

12 cm

23 cm

21.6 cm

Y


Guided practice

Guided Practice

  • Students will work on their book work, focusing only on the problems #1-7 page 241

  • Work carefully, show your problem solving process, and double check all calculations.

  • Use scratch paper to carry out your work.

  • Once you have completed the assigned problems, please raise your pencil.

  • The teacher will then check your work and release you to complete the independent practice.


Independent practice

Independent Practice

  • Once you have been signed off and released to complete Independent Practice, please complete the following assignment:

  • Finish the 5-5 Work book pages # 8-13

  • Homework:

    • Work book page 248

      • Read the directions carefully

      • Due tomorrow morning


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