1.
A conditional is a statement which can be written in: if-then form
2.
a counterexample is an example: which proves to be false
3.
a diagonal of a parallelogram: forms 2 congruent triangles
4.
A line and a plan are perpendicular: if and only if they intersect and the line is perpendicular to all the lines in the plane that pass through the point of intersection
5.
a line and a plane are parallel: if they do not intersect
6.
A line contains: at least 2 points
7.
a line that contains the midpoint of one side of a triangle and is paralel to antoher side passes: through the midpoint of the third side
8.
a parallelogram: is a quad with 2 pairs of opposite sides parallel
9.
A plane contains: at least 3 noncollinear points
10.
a rectangle: is a quad with w/ 4 right angles
11.
a rhombus: is a quad w/4 congruent sides
12.
a square: is a quad w/ 4 right angles and 4 congruent sides (only reg quad)
13.
a trapezoid: is a quad with exacly one pair of opposite sides parallel
14.
AAS Theorem: if two angles and a non-included side of one triangle are congruent to the corresponding two angles and a non-included side of a second triangle, then the triangles are congruent.
15.
ABT: If an angle is bisected,: the one angle formed measures half the measure of the total angle
16.
acute: three acute angles
17.
Acute angle: measures less than 90 more than 0 degrees
18.
Addition, Subtraction, Multiplication and Division prop of equality: allow the same operation to be performed on both sides of an equation without changing the truthfulness of the equation
19.
adjacent: share a ray, no interior points
20.
alternate interior angles: are two nonadjacent interior angles on opposite sides of the transversal
21.
altitude: is the perpendicular segment from a vertex to the line that contains the opposite side (every triangle has 3)
22.
An equilateral triangle: has three 60 degree angles
23.
An equilateral triangle: is also equiangular*
24.
an isosceles trapezoid: has 2 congruent legs
25.
angle: union of two noncollinear rays having or sharing a common endpoint
26.
ASA Postulate: If two angles and an included side of one triangle are congruent to the corresponding two angles and included side of a second triangle, then the triangles are congruent.
27.
base angles of an isosceles trapezoid: are congruent
28.
biconditional: is a statement which uses the phrase "if and only if"
29.
Bisector: a figure that intersects a segment at its midpoint
30.
Collinear points: points that lie on the same line
31.
Complementary angles: are two angles whose sum is 90 degrees
32.
Congruent: segments that have the same measure
33.
Congurent figures: have congruent corresponding parts (angles and sides)
34.
Converse: is formed by interchanging the hypothesis with the conclusion
35.
Coplaner points: points that lie on the same plane
36.
corresponding angles: are two angles in corresponding positions relative to the two lines
37.
Distributive Property of Multiplication over Addition/Subtraction: 5(x+2)=5x+10
38.
Each angle of an equiangular triangle: has measure 60
39.
equiangular: all angles congruent
40.
equilateral triangle: all sides congruent
41.
Five types of information that can be used in a proof: Postulates, theorems, definitions, given, properties
42.
For any two points,: there is a unique positive number called the distance between the points
43.
HA: if the hypotenuse and acute angle of a right triangle are congruent ot the corresponding hypotenuse and acute angle of a second right triangle, then the triangles are congruent
44.
HL Postulate: If a hypotenuse and leg of one right triangle are congruent to the corresponding hypotenuse and leg of a second right triangle, then the triangles are congruent.
45.
If a point lies on hte perpendicular bisector of a segment,: then the point is equidistant from the endpoints of the segment*
46.
If a point lies on the bisector of an angle,: then the point is equidistant from the sides of the angle*
47.
If a transversal is perpendicular to one of the two parallel lines,: then it is perpendicular to the other one also
48.
if an angle of a parallelogram is a right angle,: then the parallelogram is a rectangle
49.
if both pairs of opposite angles of a quad are congruent,: then the quad is a parallelogram
50.
if both pairs of opposite sides of a quad are congruent,: then the quad is a parallelogram
51.
if one pair of opposite sides of a quad is both congruent and parallel: then the quad is a paralleogram
52.
If one side of a triangle is longer than a second side: then the angle opposite the first side is larger than the angle opposite the second side*
53.
if the diagonals of a quad bisect each other: then the quad is a parallelogram
54.
If the exterior sides of two adjacent acute angles are perpendicular: then the angles are complementary
55.
if three parallel lines cut off congruent segments on one transversal: then the cut off congruent segments on every transversal
56.
If two angles are perpendicular: then they form congruent adjacent angles
57.
If two angles are supplements (or complements) of the same angle: then the original two angles are congruent
58.
If two angles are supplements (or complements) of two congruent angles: then the original two angles are congruent
59.
If two angles of one triangle are congruent to two angles of another triangle,: then the third angles are congruent
60.
if two consecutive sides of a parallelogram are congruent: then the parallelogram is a rhombus
61.
If two lines are cut by a transversal and alternate interior angles are congruent: then the lines are parallel
62.
If two lines are cut by a transversal and corresponding angles are congruent: then the lines are parallel
63.
If two lines are cut by a transversal and same-side interior angles are supplementary: then the lines are parallel
64.
if two lines are parallel: then all the points on one line are equidistant from the other line
65.
If two lines form congruent adjacent angles: then the lines are perpendicular
66.
If two parallel lines are cut by a transversal: then same-side interior angles are supplementary
67.
If two parallel lines are cut by a transversal: then alternate interior angles are congruent
68.
If two parallel lines are cut by a transversal,: then corresponding angles are congruent
69.
If two parallel planes are cut by a third plane: then the lines of intersection are parallel
70.
If two points lie on a plane, then: the line containing them lies on the same plane
71.
If two sides of a triangle are congruent,: then the angles opposite those sides are congruent.*
72.
In a plane two lines perpendicular to the same line are parallel: are parallel
73.
In a triangle,: there can be at most one right angle or obtuse angle
74.
Intersection: shared points, points in common
75.
isosceles triangle: at least two sides congruent
76.
LA: if a leg and acute angle of a right triangle are congruent to the corresponding leg and acute angle of a second right triangle, then the triangles are congruent.
77.
Length: subtract ends and take absolute value distance
78.
Line: shows direction, composed of points
79.
LL: if two legs of a right triangle are congruent to the corresponding two legs of a second right triagle, then the triangles are congruent.
80.
MT: If a point is a midpoint of a segment, then: one segment is half the measure of the total segment
81.
obtuse: one obtuse angle
82.
Obtuse angle: measures more than 90 less than 180
83.
parallel planes: do not intersect
84.
perpendicular bisector: is a line (ray or segment) that is perpendicular to the segment at its midpoint
85.
Perpendicular lines: are two lines that intersect to form right angles parallel lines - are coplanar lines that do not intersect
86.
Planes: flat surfaces, no thickness, no edges-infinite
87.
Point: no size, no shape, no location
88.
Points, Lines, and Planes: the only 3 undefined words in geometry
89.
Postulates: statements that are assumed to be true
90.
Ray: section of a line, have one endpoint and extending indefinitely in 1 direction
91.
Reflexive Property of Equality: AB=AB
92.
right: one right angle
93.
Right angle: measure is 90 degrees
94.
Ruler postulate: 1. free to pick scale 2. find length la-bl
95.
same-side interior angles: are two interior angles on the same side of the transversal
96.
SAS Inequality Theorem: If two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle
97.
SAS Postulate: If two sides and an included angle of one triangle are congruent to the corresponding two sides and included angle of a second triangle, then the triangles are congruent.
98.
scalene triangle: no sides congruent
99.
Segment: section of a line having 2 endpoints and all points in between
100.
Segment Addition Postulate: if B is between A and C then AB + BC= AC
101.
segments: sides of a triangle
102.
skew lines: are non coplanar lines. Neither parallel or intersection
103.
Space: set of all points
104.
space contains: at least 4 noncoplanar points
105.
SSS Inequality Theorem: If two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is longer than the third side of the second, then the included angle of the first triangle is larger than the included angle of the second.
106.
SSS Postulate: If three sides of one triangle are congrent to the corresponding three sides of a second triangle, then the triangles are congrent.
107.
straight: measures 180 degrees
108.
Substitution Property of Equality: If a=b, then a can replace b (or b replace a)
109.
Supplementary angles: are to angles who sum is 180 degrees
110.
Symmetric Property of Equality: If AB=CD then CD=AB
111.
the "if": hypothesis
112.
the "then": conclusion
113.
The acute angles of a right angle: are complementary
114.
The bisector of the vertex angle of an isosceles triangle: is perpedicular to the base at its midpoint
115.
The conditional and the converse are: independent of one another
116.
the consecutive angles of a parallelogram: are supplementary
117.
The diagonals of a parallelogram: bisect each other
118.
the diagonals of a rectangle are: congruent
119.
the diagonals of a rhomas: are perpendicular
120.
the diagonals of a rhombus: bisect opposite angles
121.
The Exterior Angle Inequality Theorem: the measure of an ext. angle of a triangle is greater than the measure of eith remoite int. angle
122.
The intersection of two lines is: exactly one point
123.
The intersection of two planes: is exactly one line
124.
The measure of an exterior angle of a triangle: equals the sum of the measures of the two remote interior angles
125.
the median of a trapezoid: 1) is parallel to the bases 2) has a length equal to the average of the base lengths
126.
the median of a trapezoid: is the segment that connects the midpoints of the legs
127.
the midpoint of the hypotenuse of a right triangle: is equidistant from the three vertices
128.
The opposite sides and opposite angles of a parallelogram: are congruent
129.
The perpendicular segment from a point to a line(or plane): is the shortest segment from the point to the point (or plane)
130.
the segment that joins the midpoints of two sides of a triangle: is parallel to the third side; is half as long as the third side
131.
The sum of the measures of the angles of a triangle: is 180
132.
The Triangle Inequality: the sum of the lengths of any two sides of a triangle is greater than the length of the third side
133.
Theorems: statements that can be proven
134.
Through a line and a point not on it, there: is exactly one plane that contains them
135.
Through a point outside a line: there is exactly one line perpendicular to the given line
136.
Through a point outside a line,: there is exactly one line parallel to the given line
137.
Through any three noncollinear points there is: exactly one plane
138.
Through any three points there is: atleast one plane
139.
Through any two points there is: exactly one line
140.
Transitive Property of Equality: If AB=CD and CD=XY, then AB=XY
141.
transversal: is a line that intersects two or more coplanar lines in different points
142.
triangle: is the figure formed by three segments joining three noncollinear points
143.
Two lines parallel to the third line: are a parallel to each other
144.
vertex pl. vertices: each of the three points of a triangle
145.
Vertical Angles: are congruent; are formed by two intersecting lines and share only a common vertex
