Compare That!

Compare That! - Page Text Content

S: By: Angela Wibrew and Angela Minelli

FC: Compare That! | Age 103 identical twins with completely different personalities!

1: Contents | 1..........Contents 2-3........Mean Proportional 4-5........McDonald's Ad 6-9........Altitude Rule 10-11.....TI-83 Calculator 12-16.....Leg Rule 17-25.....Similarity of Triangles (Proofs) 26-27.....Tutor Ad 28-31.....Twins

2: Mean Proportional | What is mean proportional? Mean proportional is also known as the "geometric mean" and is used to compare two similar triangles. | extreme = mean mean extreme

3: Remember: The product of the means equals the product of the extremes.

6: Altitude Rule | Theorem: The altitude is the mean proportional between the segments of the hypotenuse. | part of hyp. = altitude altitude other part of hyp

7: Example: Find x. | 8 | x 4

8: How to Solve: 1. Plug in the numbers for the altitude and one of the hypotenuse parts. 2. Cross multiply the proportion 3. Set the products equal to one another. 4. Once doing this, you should get the answer x=16

9: x = 8 8 4 8x8 and 4x (8)(8) = 4x 64 = 4x 4 4 | x = 16

10: GET YOUR OWN NEW TI-84!

11: Don't forget the manual!

12: Leg Rule | Theorem: The leg is the mean proportional between hypotenuse and the projection, the piece of the hypotenuse touching the given leg.

13: hypotenuse = leg leg projection

14: Steps for Solving 1. Identify the projection, the hypotenuse, and the leg. 2. Use the leg rule equation and plug the given numbers and variables in. 3. Once you have your proportion set up, cross multiply and set the two products equal to each other.

15: Solve for x | 21 | x | 5

16: hyp = leg leg proj. 21+x = 21 21 10 10(21 + x) = (21)(21) 210 + 10x = 441 -210 -210 10x = 231 10 10 | x = 23.1

17: Now to compare this to something you've already learned how to do.... PROOFS!

18: Two triangles are similar: If corresponding angles are congruent and the lengths of the corresponding sides are in proportion. (AA~AA) | ~

19: A | B | C | D | E | F | 6 10 8 | 5 3 4 | 30 | 60

20: In a proportion, the product of the means equals the product of the extremes.

21: Given: AD = AE DB EC Then: (AD)(EC) = (DB)(AE) | A D E B C

22: A line parallel to one side of a triangle cuts off a triangle that is similar to the original triangle. | A D E B C

23: A D E B C | A line parallel to one side of a triangle divides the other two sides proportionally.

24: Statements Reasons | 1. ABC & DEF,

25: Given: Triangle ABC and Triangle DEF,

26: Magazine not enough help for you? | Hire a tutor from Pythagorean's society! Only the best of the best tutors and great math assistance! | Call now 1(800)555-MATH

28: How about twins? | Real life similarities?

30: Math May Be Needed To Calculate How Old These Twins Are!!!

31: Born on November 19, 1909, Scottish twins Edith Ritchie and Evelyn Middleton are 103 years old and still living! The twins were born on a farm near Newburgh, being the youngest children in a family of nine.Age is the least of their worries! Edith and Evelyn are close to be put in the Guineas Book of World Records for oldest twins. Edith And Evelyn have more than eighty descendants! Both twins stand side by side to another till today. Twins are an amazing set of people. Having almost the exact features yet having different personalities.