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g0109

1. 1. Geometry Item 01-09 <ul><li>What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)? </li></ul><ul><ul><ul><li>scalene </li></ul></ul></ul><ul><ul><ul><li>isosceles </li></ul></ul></ul><ul><ul><ul><li>equilateral </li></ul></ul></ul><ul><ul><ul><li>equiangular </li></ul></ul></ul>www.upcatreview.com
2. 2. Don’t know how to solve it? www.upcatreview.com
4. 4. Tip #25 Educated Guess If you need to make a guess then it should be an educated guess . First, eliminate the answers that you know are wrong, then try your best to establish a basis for your choice. www.upcatreview.com
5. 5. If you know that... www.upcatreview.com
6. 6. “ Every equilateral * triangle is equiangular ** .” * Equilateral Δ = all sides are equal ** Equiangular Δ = all angles are equal www.upcatreview.com
7. 7. Then you would not choose... www.upcatreview.com
8. 8. C or D www.upcatreview.com
9. 9. Geometry Item 01-09 <ul><li>What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)? </li></ul><ul><ul><ul><li>scalene </li></ul></ul></ul><ul><ul><ul><li>isosceles </li></ul></ul></ul><ul><ul><ul><li>equilateral </li></ul></ul></ul><ul><ul><ul><li>equiangular </li></ul></ul></ul>www.upcatreview.com
10. 10. Why? www.upcatreview.com
11. 11. In a multiple choice test... www.upcatreview.com
12. 12. There is only one unique answer! www.upcatreview.com
13. 13. If you choose, say C. equilater al , www.upcatreview.com
14. 14. That means you also choose D. Equiangular ... www.upcatreview.com
15. 15. Now, it is impossible that... www.upcatreview.com
16. 16. Both C and D are correct! www.upcatreview.com
17. 17. So you are left with only two choices... www.upcatreview.com
18. 18. A or B www.upcatreview.com
19. 19. What does it mean? www.upcatreview.com
20. 20. When you still had four choices... www.upcatreview.com
21. 21. Your chance of getting the correct answer through guessing is... www.upcatreview.com
22. 22. ¼ or 25% www.upcatreview.com
23. 23. After eliminating choices C and D ... www.upcatreview.com
24. 24. Your chance of getting the correct answer from the two choices left becomes... www.upcatreview.com
25. 25. ½ or 50% www.upcatreview.com
26. 26. That simply increases your chance by 200% ! www.upcatreview.com
27. 27. Now, going back to the question... www.upcatreview.com
28. 28. Geometry Item 01-09 <ul><li>What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)? </li></ul><ul><ul><ul><li>scalene </li></ul></ul></ul><ul><ul><ul><li>isosceles </li></ul></ul></ul><ul><ul><ul><li>equilateral </li></ul></ul></ul><ul><ul><ul><li>equiangular </li></ul></ul></ul>www.upcatreview.com
29. 29. The two choices left are... www.upcatreview.com
30. 30. <ul><ul><ul><li>scalene * </li></ul></ul></ul><ul><ul><ul><li>isosceles ** </li></ul></ul></ul><ul><li>* Scalene Δ = no sides are equal </li></ul><ul><li>** Isosceles Δ = at least 2 sides are equal </li></ul>www.upcatreview.com
31. 31. Again, if you still don’t know how to solve this... www.upcatreview.com
32. 32. One technique is to draw a quick sketch of the triangle... www.upcatreview.com
33. 33. Geometry Item 01-09 <ul><li>What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)? </li></ul><ul><ul><ul><li>scalene </li></ul></ul></ul><ul><ul><ul><li>isosceles </li></ul></ul></ul><ul><ul><ul><li>equilateral </li></ul></ul></ul><ul><ul><ul><li>equiangular </li></ul></ul></ul>www.upcatreview.com
34. 34. You simply plot the vertices given (1, 1), (1, 5) and (5, 3) on the x-y plane... www.upcatreview.com
35. 35. You DON’T need an accurate drawing... www.upcatreview.com
36. 36. www.upcatreview.com 1 2 3 4 5 5 4 3 2 1 y x (1,1) (1, 5) (5, 3)
37. 37. The triangle looks like an isosceles triangle... www.upcatreview.com
38. 38. So if you really have no idea... www.upcatreview.com
39. 39. You will answer... www.upcatreview.com
40. 40. B. isosceles www.upcatreview.com
41. 41. Now, to be more confident with your “ educated guess ”... www.upcatreview.com
42. 42. Draw a horizontal line from vertex (5,3)... www.upcatreview.com
43. 43. www.upcatreview.com 1 2 3 4 5 5 4 3 2 1 y x (1,1) (1, 5) (5, 3)
44. 44. This line is perpendicular * to the vertical base of the triangle... * Perpendicular = makes 90  www.upcatreview.com
45. 45. www.upcatreview.com 1 2 3 4 5 5 4 3 2 1 y x (1,1) (1, 5) (5, 3) This is a right angle (90  ).
46. 46. This line also bisects * the vertical base... * bisector = divides into 2 equal measures www.upcatreview.com
47. 47. www.upcatreview.com 1 2 3 4 5 5 4 3 2 1 y x (1,1) (1, 5) (5, 3) This two are both 2 units long.
48. 48. Thus, the line is called a perpendicular bisector of the vertical base... www.upcatreview.com
49. 49. And any point on the perpendicular bisector of a segment has the same distance from the endpoints of the segment... www.upcatreview.com
50. 50. www.upcatreview.com 1 2 3 4 5 5 4 3 2 1 y x (1,1) (1, 5) (5, 3) This two sides are equal.
51. 51. Thus, the triangle is isosceles since it has 2 equal sides. www.upcatreview.com
52. 52. You can further verify this answer by using the Distance Formula ... www.upcatreview.com