2. Geometry 2 April 2013 1)Check your homework 2)Discuss any incorrect answers with a partner 3)Revise work as needed 4)Give yourself a grade

3. Objective Students will be able to set up and solve proportions and determine whether or not two geometric figures are similar. Students will do an investigation and solve problems.

4. Proportional? Is there a way to find the height of this statue without measuring it directly? What information Would you need? Unit Question

5. review words to know ratio- an expression that compares two quantities by division examples: a to b a:b proportion- a statement of equality between two ratios

6. practice Solve proportions: 1) 2) 3)4)

7. What makes polygons similar?

8. Is your reflection in a fun house mirror similar to a regular photo of you? Why not? In math, you can think of similar shapes as enlargements or reductions of each other with no irregular distortions!

9. Are all rectangles similar? Why or why not?

10. what about other geometric shapes? ? ? can you think of any counterexamples? similar?

11. Pg. 582 investigation 1) Read steps silently to yourself Show all steps clearly and concisely on your handout to be submitted Write answers for each step on your handout. 2) Finished? Begin problems on back. You have 10 minutes to complete the investigation.

12. words to know Congruent - same shape, same size Similar - same shape, not necessarily same size - How do you 1) same number of sides? know if 2) corresponding angles congruent? shapes are 3) corresponding sides proportional? similar? YES to all 3? They are similar! enlargements or reductions or copy of each other

13. basics of setting up proportions Think about UNITS– be consistent! must compare “same” to “same” One strategy: set up a table to organize info 1.Set up a table of information to determine what we know and what we want to find. 2.Use the information in the table to set up a proportion. see link: http://cstl.syr.edu/fipse/decunit/ratios/revprop.htm http://www.ehow.com/video_4754318_set-up-proportion- problems.html

14. practice We can use the definition of similar polygons to find missing measures - isn’t that exciting? ABCD EFGH A B find x and y E F H G C Now complete 11.1 worksheet. D 24 cm x cm 18 cm 21 cm 53 ◦ y

15. Mathematically speaking…. similarity - two polygons are similar if and only if the corresponding angles are congruent and corresponding sides are proportional. - order of the letters tells you which segments and which angles in two polygons correspond to each other - means “similar to” corresponding- same relative position See pg. 583

16. Class work practice Pg. 585 +: 7 – 9, 12, 14 Do for class work Be ready to present your work to the class.

17. Geometry 1 April 2013 1) Clean out your group folder. Place papers in the proper section of your binder. 2) Get a calculator and pencil. 3) Begin Warm Up Sheet. Do as many problems as you can in 10 minutes. 4) Listen for instruction at the end of 10 minutes.

18. Objective Students will be able to find SA and Vol of basic geometric shapes. Students will practice independently, check with a partner and work with their group. Homework due tomorrow: Complete your worksheets from today’s class. REVISIONS to Kribz and Coordinate Geometry due April 9 th. Make revisions EASY for me to find/ read!!

19. Complete Activities Listen for your name Students will work in differentiated groups to improve understanding and ability to correctly work problems working with finding Surface Area and Volume

20. Debrief Exit Quiz Find volume and surface area of a square pyramid with side length = 6 cm and slant height = 10 cm

21. Geometry 3/4 April 2013 Warm Up; verify your answer (show me the math!) 1) If then b = ? a.b. ayc. ay – x d. 2) Which of the following lengths would determine a right triangle? a. 16, 30, 34b. 50, 120, 130 c. 21, 28, 35d. all of the above

22. Semi-Finalists for KRIBZ Sarah Nichols Emma Campbell Has Thaw Prinsla Kwatemaa Leah Crawford Kate Wexler

23. A fish tank is 25 inches tall and the base is 14 by 20 inches. How much water will it take to fill the tank to a depth of 20 inches?

24. Honors Geometry 21/22 March 2012 Warm Up 1) Find the slope and midpoint of the line containing the points (-4, -6) and (12, -10). 2) Find the equation of the perpendicular bisector of the segment in #1. 3) A soda can is a cylinder with r = 3 cm and h = 12 cm. What is the volume and surface area of the can?

26. Circles and Pythagorean see page 508 conjecturedefinitionexample Tangent Conjecture a tangent to a circle is perpendicular to the radius drawn at the point of tangency “tangent” means touch at 1 point only Angles inscribed in a semicircle conjecture Angles inscribed in a semicircle are right angles. an “inscribed angle” has its vertex on the circle and its sides are chords (intersect circle at 2 points) NOTES

27. Practice 1) Find the perpendicular bisector of the segments with the following endpoints. (-5, 4) and (4, 20) 2) Find the SA and Volume of a cylinder with a radius = 4 and H = 6 3) Find the volume of a cone with r = 4, H = 8. 4) Find the area and perimeter of the parallelogram if h = 5 cm and the base = 12 inches:

28. CW: Find the surface area of the following solids Show the “net” for each, labeling dimensions Use: 1) formula 2) substitute 3) math 4) units Do page 466: 1-3, 6 Find area AND volume

29. projects REVISIONS for DSH Kribz, due April Honors Geometry 4 th Quarter Project ONLINE DETAILS- PROPOSAL APPLICATION- ONLINE Preliminaries– due April Final project due- May 8 th video, song, skit, tutorial, rap, dance…. other?

30. debrief what is surface area? how is surface area different than volume? how do you find surface area of a geometric solid?

31. area summary A parallelogram = bh A triangle = ½ bh A trapezoid =½ (b 1 +b 2 )h A kite = ½ (d 1 )(d 2 ) A regular polygon = ½ san = ½ aP π = C/d C = πd = 2πr A circle = πr 2

32. debrief what is surface area? how is surface area different than volume? how do you find surface area of a geometric solid?

33. Pythagorus in a BOX Amir’s sister is away at college and he wants to mail her a 34 inch baseball bat. The packing service sells only one kind of box, which measures 24 in x 20 in x 12 in. Will the box be big enough?? Finished? do pg. 488: Container Problem

34. you gotta know the words… http://www.mrperezonlinemathtutor.com/G/6_ 2_Surf_Area_Vol_Prisms.html

35. Using Properties of Tangents If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

36. Angle vocabulary vertexcenter Central Angle- vertex is the center of the circle. Arc measure is the central angle measure. Inscribed angle - vertex is on the circle Angles inscribed in a semi-circle semi-circle are right angles! (Triangle with the diameter as hypotenuse!) xº

37. Angles inscribed in a semi-circle Are RIGHT ANGLES http://www.mathopenref.com/semiinscribed.html

38. Perfect squares Simplify the radicals:

40. EQ- do ¼ sheet Write your name, period and “your letter” on top right corner. 1) Simplify the following radicals- do “yours” A.B. C.D. 2) Explain how to simplify a radical.

41. “The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.” debrief…can you find the errors? how many can you find? http://www.youtube.com/watch?v=DxrlcLktcxU Brain WestsideGeometry IIlustration of proof on pg. 479: http://www.youtube.com/watch?v=pVo6szYE13Y&feature=endscreen&NR=1 RIGHT RIGHT square of the hypotenuse s

42. what about surface area of regular pyramids and cones? http://www.mrperezonlinemathtutor.com/G/6_3_Surf_Area_Vol_Cones.html Consider investigations 1 and 2- pages 464- 465 Look at the sketch of a net for a pyramid HOW can you calculate the surface area? Look at the sketch for the net for a cone HOW can you calculate the surface area?

43. KNOW Area formulas: Regular PolygonsCircles Circle sectors break the area into congruent triangles

44. Term Definition Example Surface area of a prism SA = 2[1/2 bh b ] + 3 [bh side ] Surface area of a cylinder Surface area of a cone Lateral surface surface area of a pyramid Area of + Area of base sides Topbottom Lateral surface Area of 2 bases + Area of sides b h Area of base A = bh side h note: use lateral height

45. bottomLateral surface

46. debrief what is surface area? how is surface area different than volume? how do you find surface area of a geometric solid?

47. debrief how did we use Pythagorean theorem to find the relationship in the lengths of the sides of a 30-60-90 triangle? a 45-45-90? what do you need to study to be ready for a test on area?

48. Challenge Question Imagine a steel belt fitting tightly around Earth’s equator. Now imagine cutting the belt and splicing in a piece to make the belt 40 feet longer. Make the longer belt stand out evenly from the equator. (HINT- C earth ≈ 24901 miles) What’s the largest object that will fit under the belt: an atom? an ant? a large dog? an elephant? Explain your answer in complete sentences. You may make a sketch to help you think about it.

49. Large is 16 inch- $7.99 Medium is 14 inch- $5.99 Justify your answer with Math! Which is the better deal?

50. x-box method of basic factoring find two numbers that multiply to give you the top number and also add to give you the bottom given ax 2 + bx + c ac b nm find n and m so that nm = ac AND n + m = b then ax 2 + bx + c = (x + n)(x + m) ac— air conditioning goes in the “attic” b goes in the “basement”

51. using factoring to solve equations Find x if x 2 + 5x + 6 = 0 a) find the factors of the quadratic b) set EACH factor equal to ZERO and solve c) check (x + 2)(x + 3) = 0 so x + 2 = 0 OR x + 3 = 0 either would make the equation true x = -2 OR x = - 3 (-2) 2 + 5(-2) + 6 = 0 4 + -10 + 6 = 0 0 = 0√ (-3) 2 + 5(-3) + 6 = 0 9 + -15 + 6 = 0 0 = 0√

52. Geometric Probability outcome- a possible result event- a set of desired outcomes probability- the chance that something will happen, expressed as a decimal, fraction or % Probability = ----------------------------------- P(event ) means “probability of an event” # of desired outcomes total # of outcomes possible

53. 0 to 1, 0 to 100% If the outcomes are equally likely, probability (event) = # of outcomes interested in total # of possible outcomes 1.Why is the smallest probability = 0? 2.Why is the largest probability = 1 or 100% ? 3.What does a probability of 2.3 imply? 4.Does it matter if probabilities are written as fractions, decimals or percents?

54. Rug games Let’s pretend I have a rug at my house, and there is a trap door in the ceiling directly over the rug. The trap door is the same shape and size as the rug. From time to time, the trap door opens and a dart drops directly down onto the rug. The process is quite random, which means that every point of the rug has as good a chance of getting hit as any other.

55. Now, of course, my guests never sit directly on the rug (it is dangerous!), but they like to sit nearby and guess which part of the rug the next random dart will hit. To keep things interesting, I have a variety of rugs of the same size that I can put out on different occasions. Look at the first rug. Which color would you predict the dart is most likely to hit? What is P(gray)? P(white)?

56. Rug Games 1) Which color is most likely to be hit by a random falling dart? 2) Calculate the probability for each color for each rug. Remember, to be equally likely, rugs must be cut into equal size pieces. 3) What if white areas are worth 2 points, grey areas worth 3 points and black areas worth 4 points? How many points for each color would you expect to win if you played a lot of games?

57. Debrief what is probability? what must be true about the pieces to be able to calculate probability? how do you calculate probability?

58. Prove parallelogram area conjecture using 2-column or flowchart proof Given: ABCD is a parallelogram and h is an altitude.

59. Using Area Formulas Example 7 Calculate the area of the triangle below: -Draw an obtuse triangle. -Make a copy of it. -Rearrange both triangles to make a shape for which you already know the area.

60. area = ½ ( 3 )( 6 ) = 9 square units area = ½ ( 4 )( 7 ) = 14 square units area = ½ ( 5 )( 9 ) = 22 ½ square units area = ½ ( h )( b )

61. Using Properties of Kites Example 8 ABCD is a kite. Find the m  A, m  C, m  D

62. Term Definition Example Circle sector area conjecture The area of a sector of a circle is given by the formula, A is the area and r is the radius of the circle, and ‘a’ is the degree of the inscribed angle Area of a segment of a circle A = A sector - A triangle see page 453 Area of an annulus of a circle A = π R 2 - π r 2 A = A big circle - A small circle see page 453

63. video of investigation pg. 478 http://www.youtube.com/watch?NR=1&feature =endscreen&v=uaj0XcLtN5c

64. Objective Students will discover and apply methods of finding the surface area and volume of prisms and cylinders. Students will take notes and work with their group to solve problems. Need to take Friday’s test TODAY: P3: Hafsaa, David P5: Rico, Dom, Luis P6: Justin