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Honors Geometry 22 February 2013

Honors Geometry 22 February 2013. Warm up: 1) Find the base of the trapezoid if A ≈ 22.5 yd 2 a) 2 ft b) 10 ft c) 12 ft Show your work to justify your answer. 2) SOLVE for n:. h = 15 ft. 17 ft. Objective.

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Honors Geometry 22 February 2013

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  1. Honors Geometry 22 February 2013 Warm up: 1) Find the base of the trapezoid if A ≈ 22.5 yd2 a) 2 ft b) 10 ft c) 12 ft Show your work to justify your answer. 2) SOLVE for n: h = 15 ft 17 ft

  2. Objective Students will use the Pythagorean formula to solve problems and discover /apply the distance formula Students will take notes and work with their groups to solve and present problems. Homework due TODAY, February 22: Khan Academy- Proficiency in 4 skills SEE HANDOUT FOR DETAILS 1- from each column paragraph for each topic

  3. Homework due Tuesday pg. 499: 4, 5, 7 pg. 504: 2, 5, 6 pg. 509: 1 – 8 evens

  4. Need to take last week’s quiz P2: Crystal P3: Lathecia, Camille, David, Ash P5: Keyla, Allison, Dom P6: Kawther, Sophie, Nabaa, Cooper, Claire, Angelica

  5. Types of Slope Zero Negative Positive Undefined or No Slope

  6. If given 2 points on a line, you may find the slope using the formula y2 – y1 x2 – x1 ://www.youtube.com/watch?v=PPXx-43ke-g m =

  7. slope-intercept form, y = mx + b. slope y-intercept

  8. Finding the Distance Between Two Points

  9. (-6,4) (1,4) -7 -2 -1 1 3 5 7 -6 -5 -4 -3 0 4 6 8 2 Let's find the distance between two points. 7 units apart 8 7 6 So the distance from (-6,4) to (1,4) is 7. 5 4 3 2 1 -2 -3 -4 -5 -6 -7 If the points are located horizontally from each other, the y coordinates will be the same. You can look to see how far apart the x coordinates are.

  10. What coordinate will be the same if the points are located vertically from each other? (-6,4) -7 -2 -1 1 3 5 7 -6 -5 -4 -3 (-6,-3) 0 4 6 8 2 8 7 6 5 4 3 2 7 units apart 1 -2 -3 So the distance from (-6,4) to (-6,-3) is 7. -4 -5 -6 -7 If the points are located vertically from each other, the x coordinates will be the same. You can look to see how far apart the y coordinates are.

  11. But what are we going to do if the points are not located either horizontally or vertically to find the distance between them? -7 -2 -1 1 3 5 7 -6 -5 -4 -3 0 4 6 8 2 8 7 Let's start by finding the distance from (0,0) to (4,3) 6 5 4 5 3 ? 2 3 1 -2 4 -3 The Pythagorean Theorem will help us find the hypotenuse -4 -5 -6 So the distance between (0,0) and (4,3) is 5 units. -7 This triangle measures 4 units by 3 units on the sides. If we find the hypotenuse, we'll have the distance from (0,0) to (4,3) Let's add some lines and make a right triangle.

  12. Now let's generalize this method to come up with a formula so we don't have to make a graph and triangle every time. (x2,y2) (x1,y1) -7 -2 -1 1 3 5 7 -6 -5 -4 -3 0 4 6 8 2 This is called the distance formula 8 Let's start by finding the distance from (x1,y1) to (x2,y2) 7 6 5 ? 4 y2 – y1 3 2 1 x2 - x1 -2 -3 Again the Pythagorean Theorem will help us find the hypotenuse -4 -5 -6 -7 Solving for c gives us: Let's add some lines and make a right triangle.

  13. means approximately equal to -1 3 4 -5 found with a calculator CAUTION! Let's use it to find the distance between (3, -5) and (-1,4) Plug these values in the distance formula (x1,y1) (x2,y2) Don't forget the order of operations! You must do the brackets first then powers (square the numbers) and then add together BEFORE you can square root

  14. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au

  15. Chapter 9 Pythagorean Theorem

  16. Find the distance between each pair of points Find the distance between the two points: 1) 2) Required: 1) formula 2) substitution 3) do math 4) units

  17. Classwork DO page 504: 1, 3 GROUPS- 1) Each student needs to do the work on their own paper. Use graph paper. 2) Find distance and slope for each side of your quadrilateral using the formulas. Find the linear equation for the line containing each side. Groups 1 & 8: # 7 Groups 2 & 7: # 8 Groups 3 & 5: # 9 Groups 4 & 6: # 10

  18. debrief how did we use Pythagorean formula to develop the distance formula? what is easy? what is still confusing?

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