Lesson 6 1 The Parthenon represent Golden Ratio

Lesson 6 -1 The Parthenon – represent Golden Ratio Proportions Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 1

Lesson 6 -1 Proportions Ratio: A ratio is a comparison of two numbers such as a : b. When writing a ratio, always express it in simplest form. Example: A Now try to reduce the fraction. 8 10 D 4. 8 Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions C 3. 6 6 B 2

Golden Ratio ~ 1: 1. 618 ratio l The Golden Rectangle is considered to be one of the most pleasing and beautiful shapes to look at, which is why many artists have used it in their work. The two artists, who are perhaps the most famous for their use of the golden ratio, are Leonardo Da Vinci and Piet Mondrian. The Parthenon – represent Golden Ratio Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 3

Example………. A baseball player goes to bat 348 times and gets 107 hits. What is the players batting average? Solution: Set up a ratio that compares the number of hits to the number of times he goes to bat. Convert this fraction to a decimal rounded to three decimal places. The baseball player’s batting average is Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 4

Proportion: An equation that states that two ratios are equal. Terms First Term Third Term Second Term Fourth Term To solve a proportion, cross multiply the proportion: a(d) = b(c) Extremes: a and d Means : b and c Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 5

Solve each proportion. Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 6

Proportions- examples…. Example 1: Find the value of x. x 2 ft 356 yards 84 yards Example 2: Solve the proportion. 8 x = 30 8 • x = 6 • 5 x = 3. 75 8 x = 30 8 8 Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 7

Proportions- examples…. l Example 3: There are 76 boys in a sophomore class of 165 students. Find the ratio of boys to girls. Example 4: A replica of The Thinker is 10 inches tall. The replica and a statue of The Thinker, located in front of Grawemeyer Hall on the Belnap Campus of the University of Louisville have a ratio of 1: 12. What is the height of the Uof. L statue? Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 8

Proportions- examples…. Example 5: The ratio of the measures of three sides of a triangle is 9: 8: 7, and its perimeter is 144 units. Find the measure of each side of the triangle. Example 6: The ratio of the measures of three angles of a triangle 5: 7: 8. Find the measure of each angle of the triangle. Lesson 6 -1 – Proportions Lesson 5 -1: Using Proportions 9