# Geometry Honors Midterm

The flashcards below were created by user mandyg233 on FreezingBlue Flashcards.

1. undefined terms
can not be defined using other figures.

• Point
• Line
• Plane
2. Point
names a location and has no size. it is represented by a dot.

A capital letter
3. Line
a straight path that has no thickness and extends forever

A lower case letter or two points on the line
4. Plane
• a flat surface that has no thickness and extends forever.
• a script capital letter
• or
• three points not on a line.
5. collinear
points that lie on the same line
6. noncollinear
points that do not lie on the same line
7. line segment
the part of a line consisting of two points and all points between them
8. endpoint
a point at one end of a segment or the starting point of a ray

A capital letter
9. ray
part of a line that starts at an endpoint and extends forever in one direction

It's endpoint and any other point
10. Opposite Rays
two rays that have a common endpoint and form a line
11. postulate
a statement that is accepted as true without proof
12. intersection
the set of all points the two or more figures have in common
13. system of equations
a set of two or more equations containing two or more of the same variables
14. coordinate
a number used to identify the location of a point
15. distance between any two points
the absolute value of the difference of the coordinates
16. length of AB
the distance between A and B
17. Finding the Length of a Segment
| a-b | or | b-a |
18. congruent segments
segments that have the same length

uses tick marks
19. midpoint
the point that bisects, or divides the segment into two congruent segments
20. segment bisector
any ray, segment, or line that intersects a segment at its midpoint
21. angle
a figure formed by two rays, or sides, with a common endpoint
22. vertex
a common endpoint
23. How to name an angle
• Vertex
• a point on each ray and the vertex
• number

<R <SRT <1
24. interior of an angle
the set of all points between the sides of the angle
25. exterior of an angle
the set of all points outside the angle
26. the measure of an angle
the absolute value of the difference of the real numbers that the rays correspond with on a protractor
27. Acute Angle
measures greater than 0 degrees and less than 90 degrees
28. Right Angle
• Measures 90 degrees
• must have box
29. obtuse angle
measures greater than 90 degrees and less than 180 degrees
30. straight angle
• formed by two opposite rays
• measures 180 degrees
31. congruent angles
angles that have the same measure
32. angle bisector
a ray that divides an angle into two congruent angles

the (particular points) of all points in the interior of the angle that are equidistant from the sides of the angle
two angles in the same plane with a common vertex and a common side, but no common interior points
34. linear pair of angles
a pair of adjacent angles whose noncommon sides are opposite rays
35. complementary angles
two angles whose measures have a sum of 90 degrees
36. supplementary angles
two angles whose measures have a sum of 180 degrees
37. Finding the Complementary angle
90-x
38. finding the supplementary angke
180-x
39. vertical angles
two nonadjacent angles formed by two intersecting lines
40. perimeter
the sum of the side lengths of the figure

• rectangle- 2l+2w
• square- 4s
• triangle a+b+c
41. area
the number of non overlapping square units of a given size that cover the figure

• rectangle- l*w
• Square side squared
• Triangle- 1/2bh
• circle- pi(r) squared
42. base of a triangle
any side of a triangle
43. height
a segment from a vertex that forms a right angle with a line containing the base

• may be:
• inside the triangle (interior)
• outside (exterior)
• a side of the triangle
44. diameter
a segment that passes through the center of the circle and whose endpoints are on the circle
a segment whose endpoints are the center of the circle and a point on the circle
46. circumference
the distance around a circle

c=pi(d) or 2pi(r)
47. pi
irrational

3.14 or 22/7
48. coordinate plane
a plane that is divided into 4 regions by the x and y axis
49. Midpoint formula
m= (x1+x2 / 2, y1+y2 /2)
50. distance formula
d= square root of (x2-x1)2 + (y2-y1)2
51. pythagorean theorem
• ONLY in a right triangle
• used to find distance
• a2+b2=c2
52. legs of a right triangle
the 2 sides that form the right angle
53. hypotenuse
the side across from the right triangle that stretches from one leg to the other
54. transformation
a change in the position, size, or shape of a figure
55. preimage
the original figure
56. image
the resulting figure
57. ---> arrow notation
used to describe a transformation
58. ' primes
used to label the image
59. reflection (flip)
a transformation across a line, called the line of reflection.

each points and its image are the same distance from the line of reflection
60. Rotation (turn)
a transformation about a point P, called the center of rotation.

Each point and its image are the same distance from P
61. Translation (slide)
a transformation in which all the points of a figure move the same distance in the same direction
62. inductive reasoning
the process of reasoning that a rule or statement is true because specific cases are true

used to draw a conclusion from a pattern

• 1) look for a pattern
• 2) Make a conjecture
• 3) prove the conjecture or find a counterexample
63. conjecture
a statement believed to be true based on inductive reasoning
64. counterexample
an example that proves a conjecture false
65. conditional statement
a statement that can be written in the form "if p, then q"

p--> q
66. hypothesis
the part of p of a conditional statement following the word "if"
67. conclusion
the part q of a conditional statement following the word, "then"
68. truth value
true or false of a conditional statement

false when the hypothesis is true and the conclusion if false
69. negation of statement p (opposite)
~p

the negation of a true statement is false, the negation of a false statement is true
70. converse
statement formed by exchanging the hypothesis and conclusion

q-->p
71. inverse
statement formed by negating the hypothesis and the conclusion

~p--> ~q
72. contrapositive
statement formed by both exchanging and negating the hypothesis and conclusion

~q --> ~p
73. logically equivalent statements
related conditional statements that have the same truth value
74. deductive reasoning
process of using logic to draw conclusions from given facts, definitions, and properties
75. biconditional statement
a statement that can be written in the form, "p if and only if q" (iff)

if p, then q

if q, then p

used to write defintions
76. definition
a statement that describes a mathematical object and can be written as a true biconditional

iff
77. polygon
closed plane figure formed by 3 or more line segments

each segment intersects exactly two other segments only at their endpoints

no two segments with a common endpoint are collinear
78. triangle
a three sided polygon
a 4 sided polygon
80. proof
an argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true
81. theorem
any statement that you can prove
82. two column proof
proof that lists the steps of the proof in the left column and the matching reason in the right column.
83. proof process
1) write the conjecture to be proven

2) draw a diagram to represent the hypothesis of the conjecture

3) state the given information and mark it on the diagram

4) state the conclusion of the conjecture in terms of the diagram

5) plan your argument and prove the conjecture
84. flow chart proof
uses boxes and arrows to show the structures of the proof

moves from left to right or top to bottom

justification written below the box
85. paragraph proof
presents the steps of the proof and their matching reasons as sentences in a paragraph
86. parallel lines (||)
coplanar and do not intersect
87. perpendicular lines (upside down T)
intersect at 90 degree angles.
88. skew lines
are not coplanar, are not parallel, and do not intersect
89. parallel planes
planes that do not intersect
90. transversal
a line that intersects two coplanar lines at two different points

t

other 2 lines = r and s
91. corresponding angles
lie on the same side of the transversal, on the same sides of lines r and s.
92. alternate interior angles

lie on opposite sides of the transversal t, between lines r and s
93. alternate exterior angles
lie on opposite sides of the transversal t

outside lines r and s
94. same-side interior angles (consecutive interior angles)
lie on the same side of the transversal

between lines r and s
95. perpendicular bisector of a segment
a line perpendicular to a segment at the segment's midpoint
96. distance from a point to a line
the length of the perpendicular segment from the point to the line
97. rise
the difference in the y values of the 2 points on a line
98. run
the difference in the x values of 2 points on a line
99. slope
the ratio of rise to run,

m= y2-y1 / x2-x1
100. positive slope
101. negative slope
102. zero slope
103. undefined slope
104. opposite reciprocals
a/b and -b/a
105. point slope form of a line
y-y1=m(x-x1)

x1, y1 is a given point on the line
106. slope intercept form
y=mx+b

m=slope

b=y intercept
107. the equation of a vertical line
x=a

a= x intercept
108. equation of horizontal line
y=b

b= y intercept
109. y=5x+8

y=5x-4
same slope, different y intercept
110. acute triangle
three acute sides
111. equiangular triangle
3 congruent acute angles
112. right triangle
one right angle
113. obtuse triangle
one obtuse angle
114. equilateral triangle
three congruent sides
115. isosceles triangle
at least 2 congruent sides
116. scalene triangle
no congruent sides
117. auxiliary line
a line that is added to a figure to aid in a proof

-----------
118. corollary
a theorem whose proof follows directly from another theorem
119. interior
set of all points inside the figure
120. exterior
the set of all points outside the figure
121. interior angle
formed by 2 sides of a triangle
122. exterior angle
formed by one side of the triangle and the extension of an adjacent side
123. remote interior angle
an interior angle that is not adjacent to the exterior angle
124. triangle rigidity
if the side lengths of a triangle are given, the triangle can have only one shape.
125. included angle
an angle formed by two adjacent sides of a polygon
126. included side
the common side of 2 consecutive angles in a polygon
127. coordinate proof
uses coordinate geometry and algebra
128. strategies for positioning figures in the coordinate plane
use the origin as a vertex, keeping the figure in Quad I

center the figure at the origin

center a side of the figure at the origin

use one or both axes as sides of the figure
129. vertex angle
angle formed by the legs
130. base
side opposite the vertex angle
131. base angles
2 angles that have the base as a side
132. equidistant
a point is the same distance from 2 or more objects
133. concurrent
three or more lines intersect at one point
134. point of concurrency
the point where the lines intersect
135. circumcenter of a triangle
the point of concurrency in a triangle
136. circumscribed
a circle that contains all the vertices of a polygon
137. incenter of the triangle
the point of concurrency where the angle bisectors meet? (unsure)
138. inscribed
intersects each line that contains a side of the polygon at exactly one point
139. incenter
the center of the triangle's inscribed triangle

always inside the triangle
140. median of a triangle
a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side

each triangle has 3 medians, which are concurrent
141. centroid of the triangle
the point of concurrency of the medians of a triangle

always inside the triangle

center of gravity
142. altitude of a triangle
perpendicular segment from a vertex to the line containing the opposite side

each triangle has 3 altitudes

can be inside, out, or on the triangle
143. the height of a triangle is the length of an altitude
miscellaneous shit
144. orthocenter of the triangle
the point of intersection of the 3 altitudes of a triangle
145. midsegment of a triangle
segment that joins the midpoints if two sides of the triangle

every triangle has 3 midsegments, qhich form the midsegment triangle
146. indirect proof
1) identify the conjecture

2) assume the opposite of the conclusion is true

3) use direct reasoning to show that the assumption leads to a contradiction

4) conclude that since the assumption is false, the original conjecture is true
 Author: mandyg233 ID: 61768 Card Set: Geometry Honors Midterm Updated: 2011-01-25 06:36:53 Tags: Geometry Midterm Theorms Folders: Description: Cramming for the midterm is never fun. Show Answers: