# geometry FINALS

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1. a rule that is accepted without proof
postulate/axiom
2. the real number that corresponds to a point
coordinate
3. the absolute value of the difference of the coordinates of A & B
distance
4. two angles that share a common vertex & side but have no common interior points
5. two adjacent angles whose noncommon sides are opposite rays.
linear pair
6. two angles whose sides form two pairs of opposite rays
vertical angles
7. a closed plane figure
polygon
8. in a polygon if no line that contains a side of the polygon contains a point in the interior of the polygon
convex
9. a polygon that is not conves
concave
10. the distance around a fugure
perimeter
11. the distance around a circle
circumference
12. the amount of surface covered by a figure
area
13. an unproven statement based on observations
conjecture
14. find a pattern in specific cases & then write a conjecture for the general case
inductive reasoning
15. a specific case for which the conjecture is false
counterexample
16. a logical statement that has 2 parts a hypothesis & a conclusion
conditional statement
17. a statement that is the opposite of the original statement
negation
18. uses facts definitions accepted properties & laws of logic
deductive reasoning
19. a = b, then a + c = b + c
20. a = b then a - c = b - c
21. subtraction prop
22. a=b & c does not = 0 then a/c = b/c
division prop
23. a = b ac=bc
multiplication prop
24. a logical arguement that shows a statement is true.
proof
25. has numbered statements & corresponding reasons
two-column proof
26. a statement that can be proven
theorem
27. all right angles are congruent
right angles congruence theorem
28. if two angles are supplementary to the same angle (or to congruent angles) then they are congurent
• congruent supplements theorem
• same for complements
29. if two angles form a linear pair then they are supplementary
LINEAR PAIR POSTULATE
30. vertical angles are congruent
vertical angles congruence theorem
31. two lines that do not intersect & are coplanar
parllel lines
32. two lines that do not intersect & are not coplanar
skew lines
33. is there if a line and a point not on the line, then there if exactly one line through the point parallel to the given line
parallel postulate
34. if there is a line & a point not on the line, then there is exactly one line through the point perpendicular to the given line
perpendicular postulate
35. a line that intersects two or more coplanar lines & different points
transversal
36. if two lines are parallel to the same line, then they are parallel to each other
transitive property of parallel lines
37. in a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope
slopes of parallel lines
38. two nonvertical lines are perpendicular if & only if the product of their slopes id -1
slopes of perpendicular lines
39. if a transversal is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other
perpendicular transversal theorem
40. in a plane if two lines are perpendicular to the same line, then they are parallel to each other
lines perpendicular to a transversal theorem
41. the original angles
interior angles
42. the angles that form linear pairs w/ the interior angles are the
exterior angles
43. the sum of the measures of the interior angles of a triangle is 180
triangle sum theorem
44. the measure of an exterior angle of a triangle is = tot he sum of the measures of the two nonadjacent interior angles
exterior angle theorem
45. a statement that can be proved easily using the theorem
corollary to a theorem
46. the acute angles of a right angle are complementary
corollary to the triangle sum theorem
47. if two angles of one triangle are congruent to two angles of another triangle, then the 3rd angles are also congruent
third angles theorem
48. if two sides of a triangle are congruent then the angles opposite them are congruent
base angles theorem
49. if two angles of a triangle are congruent then the angles opposite them are congruent
converse of base angles theorem
50. if a triangle if equilateral then it is equiangular
corollary to the base angles theorem
51. if a triangle is equiangular, then it is equilateral
corollary to the converse of base angles theorem
52. an operation that moves or changes a geometric figure in some way to produce a new figure
transformation
53. the new figure
image
54. moves every point of a figure the same direction & distance
translation
55. uses a line of reflection to create a mirror image of the original figure
reflection
56. turns a fig. around a fixed point
rotation
57. a segment that connects the midpoints of two sides of the triangle
midpoint of the triangle
58. the segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side & is half as long as that side
midsegment theorem
59. a seg., ray, line, or plane that is perpendicular to a segment @ its midpoint
perpendicular bisector
60. same distance form each point
equidistant
61. in a plane if a point is on the perpendicular bisector of a seg. then it is equidistant from the endpoints of the seg.
perpendicular bisector theorm
62. in a plane if a point is equidistant from the endpoints of a seg. then it is on the perpendicular bisector of the segment
converse of the perpendicular bisector theorem
63. when three or more lines,rays, or segs. intersect in the same point
• concurrent
• the point is the point of concurrency
64. the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle
concurrency of perpendicular bisectors of a triangle
65. the point of concurrency of the 3 perpendicular bisectors
circumcenter
66. if a point is on the bisector of an angle, then it is equidistant form the two sides of the angle
angle bisector theorem
67. if a point is in the interior of an angle & is equidistant from the sides of the angle then it lies on the bisector of the angle
converse of the angle bisector theorem
68. the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle
concurrency of angle bisectors of a triangle
69. the point of concurrency of the 3 angle bisectors of a triangle
incenter
70. a segment from a vertex to the midpoint of the opposite side.
median of triangle
71. point of concurrency of the medians of a triangle
centroid
72. the medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.
concurrency of medians of a triangle
73. the perpendicular segment from vertex to the opposite side or line that contains the opposite side
altitude of a triangle
74. the lines containing the altitudes of a triangle are concurrent
concurrency of altitudes of a triangle
75. the point of concurrency for ltitudes
orthocenter
76. the sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side
triangle inequality theorem
77. if two sides of one triangle are congruent to two sides of another triangle & the includes angle of the 1st is larger than the included angle of the 2nd then the third side of the 1st is longer then the 3rd of the second
hinge theorem
78. if two sides of one triangle are congruent to two sides of another triangle & the third side of the first is longer than the third side of the second then the included angle of the first is larger than the included angle of the second
converse of the hinge theorem
 Author: brendabelle ID: 55351 Card Set: geometry FINALS Updated: 2010-12-12 22:14:30 Tags: geometry Folders: Description: finals Show Answers: