Chapter 5 : Ratios, Rates & Proportions Section 5

1 / 17

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

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about 'Chapter 5 : Ratios, Rates & Proportions Section 5' - cher

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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 =2/4 a/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/d b 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