Clickers Bellwork A stack of 100 nickels is 6.25 inches high. To the nearest cent, how much would a stack of nickels 8 feet high be worth?

Bellwork A stack of 100 nickels is 6.25 inches high. To the nearest cent, how much would a stack of nickels 8 feet high be worth?

Use Similar Polygons Section 6.3

The Concept Yesterday we reviewed ratios and proportions and also talked about the relationship between two objects Now we’re going to suffuse the two concepts into a practical application of similar polygons

Scale Factor Scale factor is the scalar multiplier used to relate similar objects Scale factor is typically used when discussing maps, blueprints or even models of buildings or cars

Important Points When we talk about scale factor it is important to be cognizant of two important points Scale factor is found through the ratio of the second object to the first “Scaling” a polygon only effects the side length, not the angle measure 2 1 6 12 Scale factor of 2 5 10 4 8 60o 60o 5 10 30o 30o

Example What’s the scale factor between these two objects? 42 12 35 10 8 28

Example What’s the scale factor between these two objects? 20 14 10 7 6 16 3 8

Example The object on the left is scaled by a factor of 4.75. What is the length of the corresponding side to AB of the new figure? D 15 11 C A 16 19 B

Terminology Congruence Similar When two objects are scaled, they are considered similar objects Similarity The relationship between two or more two dimensional figures via a common ratio In fact, we can explain congruence as a similarity with a common ratio of 1 This can be seen in the notation for similarity vs. congruence And by the fact that we utilize similar jargon, such as corresponding parts Congruence Similar

Example Write the similarity statement for these two objects? C D B E

Further Relationships What’s the ratio between these two triangles? B E 15 10 9 6 A C D 12 F 8 Does this ratio hold true for perimeters

Perimeter Theorem Theorem 6.1: Perimeters of Similar Polygons If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths

Example What’s the perimeter of object 2? 22 14 8 18 4

Example What’s the perimeter of object 2? Object 2 15 11 22 16 19

Practical Example You are constructing a rectangular play area. You are basing your dimensions on a similar playground that has a length of 25m and a width of 15m. Your play area will only be 10m in length. How much fencing will you have to buy for your new play area?

Analysis Billy Joe has a rectangular pasture with a perimeter of 1500ft. He likes to show off his mathematical abilities to his friends Daryl and Darrell, by explaining that his pole barn is exactly 20% the size of his pasture. What is the perimeter of his pole barn? Unfortunately, a new survey was done on Billy Joe’s land and showed that the cornerstone had moved and his property line was actually 25 feet in on one of the sides (the whole line moved). Can he still make the claim about his pole barn?

Homework 6.3 1-8, 9-27 odd, 30-32

Example Find the missing dimensions ΔABC~ΔDEF ΔABC is equilateral B 10

Most Important Points Using ratios in geometric relationships