# Chapter 5 : Ratios, Rates & Proportions Section 5 - PowerPoint PPT Presentation

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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

Using Similar Figures

### 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

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

### 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?

• 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

• 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).

### 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

• +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

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

• 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

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

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

### C4U Question #1Checking for Understanding

• Question #1:

-The 2 Triangles are Similar.

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

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 #2Checking for Understanding

• Question #2:

-The 2 Triangles are Similar.

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

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 #3Checking for Understanding

• Question #3:

-The 2 Triangles are Similar.

-What is the value of the Missing Measure?

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 #4Checking for Understanding

• Question #4:

-The 2 Parallelograms are Similar.

-What is the value of the Missing Measure?

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

• 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

• 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