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>...
Don’t know how to solve it? www.upcatreview.com
This tip might help you... www.upcatreview.com
Tip #25  Educated  Guess If you need to make a guess then it should be an  educated guess . First,  eliminate  the answers...
If you know that... www.upcatreview.com
“ Every equilateral *  triangle is equiangular ** .” * Equilateral  Δ  = all sides are equal ** Equiangular  Δ  = all angl...
Then you would not choose... www.upcatreview.com
C or D www.upcatreview.com
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>...
Why? www.upcatreview.com
In a multiple choice test... www.upcatreview.com
There is only one unique answer! www.upcatreview.com
If you choose, say C. equilater al , www.upcatreview.com
That means you also choose D. Equiangular ... www.upcatreview.com
Now, it is impossible that... www.upcatreview.com
Both  C  and  D  are correct! www.upcatreview.com
So you are left with only two choices... www.upcatreview.com
A  or  B www.upcatreview.com
What does it mean? www.upcatreview.com
When you still had four choices... www.upcatreview.com
Your chance of getting the correct answer through guessing is... www.upcatreview.com
¼  or  25% www.upcatreview.com
After eliminating choices  C  and  D ... www.upcatreview.com
Your chance of getting the correct answer from the two choices left becomes... www.upcatreview.com
½  or  50% www.upcatreview.com
That simply increases your chance by 200%  ! www.upcatreview.com
Now, going back to the question... www.upcatreview.com
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>...
The two choices left are... www.upcatreview.com
<ul><ul><ul><li>scalene * </li></ul></ul></ul><ul><ul><ul><li>isosceles ** </li></ul></ul></ul><ul><li>* Scalene  Δ  = no ...
Again, if you still don’t know how to solve this... www.upcatreview.com
One technique is to draw a quick sketch of the triangle... www.upcatreview.com
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>...
You simply plot the vertices given  (1, 1), (1, 5) and (5, 3)  on the x-y plane... www.upcatreview.com
You  DON’T  need an accurate drawing... www.upcatreview.com
www.upcatreview.com 1  2  3  4  5 5 4 3   2   1 y x (1,1) (1, 5) (5, 3)
The triangle looks like an isosceles triangle... www.upcatreview.com
So if you really have no idea... www.upcatreview.com
You will answer... www.upcatreview.com
B. isosceles www.upcatreview.com
Now, to be more confident with your “ educated guess ”... www.upcatreview.com
Draw a horizontal line from vertex (5,3)...  www.upcatreview.com
www.upcatreview.com 1  2  3  4  5 5 4 3   2   1 y x (1,1) (1, 5) (5, 3)
This line is perpendicular *  to the vertical base of the triangle... * Perpendicular  = makes 90  www.upcatreview.com
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  ).
This line also bisects *  the vertical base... * bisector  = divides into 2 equal measures www.upcatreview.com
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.
Thus, the line is called a  perpendicular bisector  of the vertical base... www.upcatreview.com
And any point on the perpendicular bisector of a segment has the  same distance  from the  endpoints  of the segment...  w...
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.
Thus, the triangle is  isosceles   since it has 2 equal sides. www.upcatreview.com
You can further verify this answer by using the  Distance Formula ... www.upcatreview.com
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  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
  3. 3. This tip might help you... 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

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