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Section 8.1 Appetizers (Do now, please.)

P. E. A. P. N. T. E. A. Q. N. T. Section 8.1 Appetizers (Do now, please.) Given: PENTA is a regular pentagon Prove: PNT is isosceles Given: PENTA is a regular pentagon PQ is the perpendicular bisector to NT Prove: PQ passes through P. Section 8.1 Ratio and Proportion

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Section 8.1 Appetizers (Do now, please.)

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  1. P E A P N T E A Q N T Section 8.1Appetizers (Do now, please.) Given: PENTA is a regular pentagonProve: PNT is isosceles Given: PENTA is a regular pentagon PQ is the perpendicular bisector to NTProve: PQ passes through P

  2. Section 8.1Ratio and Proportion • By the end of this lesson you will be able to: • Work with ratios and proportions(this should be a review from algebra) • Apply the product and ratio theorems • Calculate geometric means

  3. Section 8.1Review In an equiangular polygon, the measure of each exterior angle is 20% of the measure of each interior angle. What is the name of the polygon?

  4. Definition: A ratio is a quotient of two numbers. Definition: A proportion is an equation stating that two or more ratios are equal.

  5. What You Already Know . . . Definition: In a proportion containing four terms, the first and fourth (a and d) are called the extremes. The second and third terms (b and c) are called the means.

  6. Product and Ratio Theorems Theorem: In a proportion, the product of the means is equal to the product of the extremes. (Means-Extremes Product Theorem) cross-multiplication Theorem: If the product of a pair of non-zero numbers is equal to the product of another pair of non-zero numbers, then either pair of numbers may be made the extremes, and the other pair the means, of a proportion. (Means-Extremes Ratio Theorem) cross-multiplication in reverse

  7. Geometric Mean In a mean proportion, the means are the same. Definition: If the means in a proportion are equal, either mean is called a geometric mean, or mean proportional between the extremes. Definition: The average between two numbers is called the arithmetic mean.

  8. Homework ?

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