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• 1. Geometry Item #009
• What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)?
• scalene
• isosceles
• equilateral
• equiangular
www.upcatreview.com
• 2. Don’t know how to solve it? www.upcatreview.com
• 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. If you know that... www.upcatreview.com
• 6. “ Every equilateral * triangle is equiangular ** .” * Equilateral Δ = all sides are equal ** Equiangular Δ = all angles are equal www.upcatreview.com
• 7. Then you would not choose... www.upcatreview.com
• 8. C or D www.upcatreview.com
• 9. Geometry Item #009
• What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)?
• scalene
• isosceles
• equilateral
• equiangular
www.upcatreview.com
• 10. Why? www.upcatreview.com
• 11. In a multiple choice test... www.upcatreview.com
• 12. There is only one unique answer! www.upcatreview.com
• 13. If you choose, say C. equilater al , www.upcatreview.com
• 14. That means you also choose D. Equiangular ... www.upcatreview.com
• 15. Now, it is impossible that... www.upcatreview.com
• 16. Both C and D are correct! www.upcatreview.com
• 17. So you are left with only two choices... www.upcatreview.com
• 18. A or B www.upcatreview.com
• 19. What does it mean? www.upcatreview.com
• 20. When you still had four choices... www.upcatreview.com
• 21. Your chance of getting the correct answer through guessing is... www.upcatreview.com
• 22. ¼ or 25% www.upcatreview.com
• 23. After eliminating choices C and D ... www.upcatreview.com
• 24. Your chance of getting the correct answer from the two choices left becomes... www.upcatreview.com
• 25. ½ or 50% www.upcatreview.com
• 26. That simply increases your chance by 200% ! www.upcatreview.com
• 27. Now, going back to the question... www.upcatreview.com
• 28. Geometry Item #009
• What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)?
• scalene
• isosceles
• equilateral
• equiangular
www.upcatreview.com
• 29. The two choices left are... www.upcatreview.com
• 30.
• scalene *
• isosceles **
• * Scalene Δ = no sides are equal
• ** Isosceles Δ = at least 2 sides are equal
www.upcatreview.com
• 31. Again, if you still don’t know how to solve this... www.upcatreview.com
• 32. One technique is to draw a quick sketch of the triangle... www.upcatreview.com
• 33. Geometry Item #009
• What type of triangle is the one with vertex coordinates (1, 1), (1, 5) and (5, 3)?
• scalene
• isosceles
• equilateral
• equiangular
www.upcatreview.com
• 34. You simply plot the vertices given (1, 1), (1, 5) and (5, 3) on the x-y plane... www.upcatreview.com
• 35. You DON’T need an accurate drawing... www.upcatreview.com
• 36. www.upcatreview.com 1 2 3 4 5 5 4 3 2 1 y x (1,1) (1, 5) (5, 3)
• 37. The triangle looks like an isosceles triangle... www.upcatreview.com
• 38. So if you really have no idea... www.upcatreview.com
• 39. You will answer... www.upcatreview.com
• 40. B. isosceles www.upcatreview.com
• 41. Now, to be more confident with your “ educated guess ”... www.upcatreview.com
• 42. Draw a horizontal line from vertex (5,3)... www.upcatreview.com
• 43. www.upcatreview.com 1 2 3 4 5 5 4 3 2 1 y x (1,1) (1, 5) (5, 3)
• 44. This line is perpendicular * to the vertical base of the triangle... * Perpendicular = makes 90  www.upcatreview.com
• 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. This line also bisects * the vertical base... * bisector = divides into 2 equal measures www.upcatreview.com
• 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. Thus, the line is called a perpendicular bisector of the vertical base... www.upcatreview.com
• 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. 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. Thus, the triangle is isosceles since it has 2 equal sides. www.upcatreview.com
• 52. You can further verify this answer by using the Distance Formula ... www.upcatreview.com