Geometry: Midterm Review Flashcards
(294 cards)
0
Q
Acute triangle
A
All angles are acute
1
Q
Polygon Exterior Angle-Sum Theorem
A
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
2
Q
Plane
A
A flat surface that has no thickness. Contains many lines and extends without end in the direction of all its lines
3
Q
same-side interior angles
A
- same side as t
* between L1 and L2
4
Q
Complementary angles
A
Two angles whose measures have the sum of 90
5
Q
Theorem 4-5
A
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base
6
Q
Reflexive Property of Equality
A
a = a
7
Q
corresponding angles
A
- same side of t
* both above or both below L1 and L2
8
Q
Converse of the Angle Bisector Theorem
A
If a point in the interior of an angle is equidistance from the sides of the angle, then the point is on the angle bisector.
9
Q
Deductive reasoning
A
The process of reasoning logically from given statements to a conclusion.
10
Q
Spherical Geometry Parallel Postulate
A
Through a point not on a line, there is no line parallel to the given line.
11
Q
Circumcenter
A
The point of concurrency of the perpendicular bisectors of a triangle.
12
Q
alternate exterior angles
A
- opposite sides of t
- outside L1 and L2
- non-adjacent
13
Q
The Distributive Property
A
a(b + c) = ab + ac
14
Q
Counterexample
A
A particular example or instance that makes a statement false
15
Q
Equilateral triangle
A
Triangle where all sides are congruent.
16
Q
Congruent Supplements Theorem
A
If two angles are supplements of the same angle, then the two angles are congruent.
17
Q
Coplanar
A
Points and line in the same plane
18
Q
Law do Detachment
A
If a conditional is true and its hypothesis is true, then it’s conclusion is true.
19
Q
Theorem 5-10
A
If two sides of a triangle are not congruent, then the longer side lies opposite the larger angle.
20
Q
Negation
A
A statement that had the opposite meaning of the original statement.
21
Q
Corollary
A
A statement that follows immediately from a theorem
22
Q
Polygon Exterior Angle-Sum Theorem
A
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
23
Q
SSS Postulate
A
Side side side
24
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half its length.
25
Vertical angles
Two angles whose sides form two pairs of opposite rays.
26
alternate exterior angles
* opposite sides of t
* outside L1 and L2
* non-adjacent
27
Angle
Two rays with a common endpoint
28
Addition Property of Equality
If a=b, then a+c = b+c
29
Triangle Angle-Sum Theorem
The sum of the measure of a triangle is 180.
30
Convex polygon
A polygon with no diagonal points on the outside
31
Congruent Complements Theorem
A. If two angles are complements of the same angle, then the two angles are congruent.
B. All right angles are congruent.
C. If two angles are congruent and supplementary, then each is a right angle.
32
Corresponding Angles Postulate
If a transversal intersects two parallel lines, the corresponding angles are congruent.
33
CPCTC
Corresponding parts of congruent triangles are congruent
34
Angle Addition Postulate
Same as Segment Addition Postulate but with angles
35
same-side interior angles
* same side as t
| * between L1 and L2
36
Exterior angle of a polygon
An angle formed by a side and an extension of an adjacent side of a polygon.
37
Convex polygon
A polygon with no diagonal points on the outside
38
Standard form of a linear equation
Ax + By = C
A, B, C are real numbers
A and B are not zero
39
Corollary to the Isosceles Triangle Theorem
If a triangle is equilateral, then the triangle is equiangular
40
Perpendicular Bisectors Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistance from the end points of the segment.
41
Substitution Property of Equality
If a = b! then b can replace a in any expression.
42
Theorem 4-1
If the two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
43
Postulate 1-2
If two lines intersect, then they intersect in exactly one point.
44
Space
The set of all points
45
Corresponding Angles Postulate
If a transversal intersects two parallel lines, the corresponding angles are congruent.
46
Concurrent
When three or more lines intersect in one point.
47
Law of Syllogism
If p --> q and q --> r are true statements, then p --> r is a true statement
48
Postulate 1-3
If two planes intersect, then they intersect in exactly one line.
49
Conclusion
The part of a conditional following "then"
50
Truth value
A conditional can be true or false
51
Polygon
A closed plane figure with at least three sides that are segments.
52
Postulate 1-1
Through any two points there is exactly one line
53
Protractor Postulate
You can measure an angle using a protractor
54
Midpoint
A point that divides a segment into two congruent segments
55
Indirect proof
A proof involving indirect reasoning.
56
Straightedge
A ruler with no markings on it
57
alternate interior angles (AIA)
* opposite sides of t
* between L1 and L2
* non-adjacent
58
Inverse
The _________ of the conditional "if p, then q" is the conditional "if not p, then not q"
59
Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC
60
Ray
A set of points with one endpoint and extends infinitely in the other direction
61
Corollary to the Isosceles Triangle Theorem
If a triangle is equilateral, then the triangle is equiangular
62
SAS Postulate
Side angle side
63
Collinear points
Points that lie on the same line
64
Theorem 3-6
If two lines are perpendicular to the same line, then they are parallel to each other
65
Postulate 1-10
The area of a region is the sum of the areas of it's nonoverlapping parts
66
Scalene
Triangle with no congruent sides.
67
Postulate 1-4
Through any three noncollinear points there is exactly one plane.
68
Concave polygon
A polygon with at least one diagonal with points on the outside.
69
Isosceles Triangle Theorem
If two sides of a triangle are congruent, the the angles opposite those sides are congruent.
70
Converse of the Same-Side Interior Angles Theorem
If two lines and a transversal form same-side interior angles that are supplementary, the the two lines are parallel.
71
Orthocenter
The point of intersection of the lines containing the altitudes of the triangle.
72
Altitude
The perpendicular segment from a vertex to the line containing the opposite side.
73
Same-Side Interior Angles Theorem
If a transverse intersects two parallel lines, then same-side interior angles are supplementary.
74
Alternate Interior Angles Theorem
If a transverse intersects two parallel lines, then alternate interior angles are congruent.
75
Slope-intercept form
y = mx + b
m is the slope of the line
b is the y-intercept
76
Theorem 5-10
If two sides of a triangle are not congruent, then the longer side lies opposite the larger angle.
77
alternate interior angles (AIA)
* opposite sides of t
* between L1 and L2
* non-adjacent
78
Isosceles
Triangle with at least two congruent sides.
79
Isosceles Triangle Theorem
If two sides of a triangle are congruent, the the angles opposite those sides are congruent.
80
Remote interior angles
The two nonadjacent interior angles corresponding to each exterior angle of a triangle.
81
Hypotenuse
The side opposite the right angle that is the longest
82
Converse of the Alternate Interior Angles Theorem
If toe lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.
83
Parallel Postulate
Through a point not on a line, there is one and only one line parallel to the given line.
84
Congruent segments
Two segments with the same length
85
SSS Postulate
Side side side
86
Equivalent statements
Statements with the same truth value.
87
Supplementary angles
Two angles whose measures have the sum of 180
88
Postulate or axiom
Accepted statement of fact
89
Postulate 1-3
If two planes intersect, then they intersect in exactly one line.
90
Theorem
The statement you prove true using deductive reasoning.
91
HL Theorem
Hypotenuse Leg Theorem
92
Polygon Angle-Sum Theorem
The sum of the measures of the angles of a n-gon is (n-2)180
93
Triangle Angle-Sum Theorem
The sum of the measure of a triangle is 180.
94
Median
A segment whose end points are a vertex and the midpoint of the opposite side.
95
Two-column proof
A proof where statements and reasons are aligned in columns.
96
Point
A location; has no size; represented by a small dot and is named by a capital letter.
97
Regular polygon
Polygon that is both equilateral and equiangular.
98
Angle Addition Postulate
Same as Segment Addition Postulate but with angles
99
Parallel lines
Coplanar lines that never intersect
100
CPCTC
Corresponding parts of congruent triangles are congruent
101
Standard form of a linear equation
Ax + By = C
A, B, C are real numbers
A and B are not zero
102
Conditional
An if-then statement
103
Theorem 5-6
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistance from the vertices.
104
Theorem 3-5
In a plane, if two lines are parallel to the same line, then they are parallel to each other.
105
Converse of the Same-Side Interior Angles Theorem
If two lines and a transversal form same-side interior angles that are supplementary, the the two lines are parallel.
106
Skew lines
Noncoplanar lines that never intersect
107
Adjacent angles
To coplanar angles with a common side, a common vertex, and no common interior points.
108
Theorem 5-9
The lines that contain the altitudes of a triangle are concurrent.
109
Slope-intercept form
y = mx + b
m is the slope of the line
b is the y-intercept
110
Postulate 1-1
Through any two points there is exactly one line
111
Polygon Angle-Sum Theorem
The sum of the measures of the angles of a n-gon is (n-2)180
112
Segment
The part is a line consisting of two end points and all points between them
113
Converse of the Alternate Interior Angles Theorem
If toe lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.
114
Right triangle
Triangle with one right angle.
115
Incenter
The point of concurrency of the angle bisectors of a triangle.
116
Regular polygon
Polygon that is both equilateral and equiangular.
117
Midsegment
The segment that joins the midpoints o two sides of a triangle.
118
Inductive reasoning
Reasoning that is based on patterns you observe
119
Conjecture
A conclusion you reach using inductive reasoning
120
Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite the angles are congruent
121
transversal
A line that intersects two coplanar lines at two distinct points.
122
Theorem 3-5
In a plane, if two lines are parallel to the same line, then they are parallel to each other.
123
Parallel Postulate
Through a point not on a line, there is one and only one line parallel to the given line.
124
Theorem 4-1
If the two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
125
Protractor Postulate
You can measure an angle using a protractor
126
Equiangular polygon
Polygon with all congruent angles
127
Theorem 4-5
The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base
128
Equilateral triangle
Triangle where all sides are congruent.
129
Converse
Switches the hypothesis and conclusion of a conditional
130
Postulate 1-10
The area of a region is the sum of the areas of it's nonoverlapping parts
131
Congruent angles
Angles with the same measure
132
Contrapositive
Switches the hypothesis and the conclusion of a conditional and negates both.
133
Equiangular triangle
All angles are congruent
134
Postulate 1-2
If two lines intersect, then they intersect in exactly one point.
135
Angle bisector
A ray that divides an angle into two congruent coplanar angles
136
Centroid
The point of concurrency of the medians.
137
Corollary to the Converse of the Isosceles Triangle Theorem
If a triangle is equilateral, then it is equiangular
138
Converse of the Perpendicular Bisector Theorem
If a point is equidistance from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
139
Obtuse triangle
Triangle with one obtuse angle
140
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
141
Postulate 1-9
If two figures are congruent, then their areas are congruent.
142
Scalene
Triangle with no congruent sides.
143
Right triangle
Triangle with one right angle.
144
Theorem 5-7
The bisector of the angles of a triangle are concurrent at a point equidistance from the sides.
145
Obtuse triangle
Triangle with one obtuse angle
146
Hypotenuse
The side opposite the right angle that is the longest
147
Straight angle
x = 180
148
Segment Addition Postulate
If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC
149
Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
150
HL Theorem
Hypotenuse Leg Theorem
151
Opposite rays
Two collinear rays with the same endpoint
152
Vertical Angles Theorem
Vertical angles are congruent.
153
Perpendicular lines
Two lines that intersect to form right angles
154
Flow proof
A proof where arrows show the logical connections between the statements.
155
Converse of the Corresponding Angles Postulate
If two lines and a transversal form corresponding angles that are congruent, the the two lines are parallel.
156
Multiplication Property of Equality
If a = b! then a x c = b x c
157
Equilateral polygon
Polygon with all congruent sides
158
Ruler postulate
A segment can be measured with a ruler
159
Exterior angle of a polygon
An angle formed by a side and an extension of an adjacent side of a polygon.
160
Transitive Property of Equality
If a = b and b = c, then a = c
161
Two-column proof
A proof where statements and reasons are aligned in columns.
162
Angle Bisector Theorem
If a point is on the bisector of an angle, the the point is equidistance from the sides of the angle.
163
Subtraction Property of Equality
If a=b, then a - c = b - c
164
SAS Postulate
Side angle side
165
Converse of the Corresponding Angles Postulate
If two lines and a transversal form corresponding angles that are congruent, the the two lines are parallel.
166
Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
167
Converse of the Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite the angles are congruent
168
Postulate 1-4
Through any three noncollinear points there is exactly one plane.
169
Symmetric Property of Equality
If a = b, then b = a
170
Alternate Interior Angles Theorem
If a transverse intersects two parallel lines, then alternate interior angles are congruent.
171
Perpendicular bisector
A line, segment, or ray that is perpendicular to a segment at its midpoint
172
Theorem 3-6
If two lines are perpendicular to the same line, then they are parallel to each other
173
Equiangular triangle
All angles are congruent
174
Paragraph proof
A proof written as sentences in a paragraph
175
Division Property of Equality
If a = b and c does not = 0, then a/c = b/c
176
Theorem 5-7
The bisector of the angles of a triangle are concurrent at a point equidistance from the sides.
177
Biconditional
The combination of a conditional statement and its converse. Contains the words "if and only if"
178
Ruler postulate
A segment can be measured with a ruler
179
Indirect reasoning
All possibilities are considered and then all but one are proved false. The remaining possibility must be true.
180
Acute triangle
All angles are acute
181
Polygon
A closed plane figure with at least three sides that are segments.
182
Equilateral polygon
Polygon with all congruent sides
183
Theorem 5-8
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.
184
Remote interior angles
The two nonadjacent interior angles corresponding to each exterior angle of a triangle.
185
Spherical Geometry Parallel Postulate
Through a point not on a line, there is no line parallel to the given line.
186
Corollary to the Converse of the Isosceles Triangle Theorem
If a triangle is equilateral, then it is equiangular
187
Isosceles
Triangle with at least two congruent sides.
188
Theorem 5-6
The perpendicular bisectors of the sides of a triangle are congruent at a point equidistance from the vertices.
189
Equiangular polygon
Polygon with all congruent angles
190
Right angle
x = 90
191
Obtuse angle
90 < x < 180
192
Point of concurrency
The point at which concurrent lines intersect.
193
Line
A series of points that extends in two opposite directions without end
194
Corollary
A statement that follows immediately from a theorem
195
Theorem 5-8
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.
196
transversal
A line that intersects two coplanar lines at two distinct points.
197
Acute angle
0 < x < 90
198
Theorem 5-9
The lines that contain the altitudes of a triangle are concurrent.
199
Same-Side Interior Angles Theorem
If a transverse intersects two parallel lines, then same-side interior angles are supplementary.
200
Hypothesis
The part of a conditional following "if"
201
corresponding angles
* same side of t
| * both above or both below L1 and L2
202
Comparison Property of Inequality
If a = b + c and c > 0, then a > b
203
Flow proof
A proof where arrows show the logical connections between the statements.
204
Parallel planes
Planes that do not intersect
205
Postulate 1-9
If two figures are congruent, then their areas are congruent.
206
Concave polygon
A polygon with at least one diagonal with points on the outside.
207
Theorem 5-7
The bisector of the angles of a triangle are concurrent at a point equidistance from the sides.
208
Comparison Property of Inequality
If a = b + c and c > 0, then a > b
209
Theorem 5-10
If two sides of a triangle are not congruent, then the longer side lies opposite the larger angle.
210
Angle Bisector Theorem
If a point is on the bisector of an angle, the the point is equidistance from the sides of the angle.
211
Theorem 5-6
The perpendicular bisectors of the sides of a triangle are congruent at a point equidistance from the vertices.
212
Theorem 5-9
The lines that contain the altitudes of a triangle are concurrent.
213
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
214
Theorem 5-8
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.
215
Theorem 5-9
The lines that contain the altitudes of a triangle are concurrent.
216
Converse of the Perpendicular Bisector Theorem
If a point is equidistance from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
217
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half its length.
218
Theorem 5-6
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistance from the vertices.
219
Theorem 5-8
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.
220
Converse of the Angle Bisector Theorem
If a point in the interior of an angle is equidistance from the sides of the angle, then the point is on the angle bisector.
221
Theorem 5-10
If two sides of a triangle are not congruent, then the longer side lies opposite the larger angle.
222
Theorem 5-7
The bisector of the angles of a triangle are concurrent at a point equidistance from the sides.
223
Perpendicular Bisectors Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistance from the end points of the segment.
224
Orthocenter
The point of intersection of the lines containing the altitudes of the triangle.
225
Inverse
The _________ of the conditional "if p, then q" is the conditional "if not p, then not q"
226
Point of concurrency
The point at which concurrent lines intersect.
227
Indirect proof
A proof involving indirect reasoning.
228
Median
A segment whose end points are a vertex and the midpoint of the opposite side.
229
Incenter
The point of concurrency of the angle bisectors of a triangle.
230
Indirect reasoning
All possibilities are considered and then all but one are proved false. The remaining possibility must be true.
231
Negation
A statement that had the opposite meaning of the original statement.
232
Equivalent statements
Statements with the same truth value.
233
Centroid
The point of concurrency of the medians.
234
Circumcenter
The point of concurrency of the perpendicular bisectors of a triangle.
235
Concurrent
When three or more lines intersect in one point.
236
Contrapositive
Switches the hypothesis and the conclusion of a conditional and negates both.
237
Altitude
The perpendicular segment from a vertex to the line containing the opposite side.
238
Midsegment
The segment that joins the midpoints o two sides of a triangle.
239
Conditional
An if-then statement
240
Biconditional
The combination of a conditional statement and its converse. Contains the words "if and only if"
241
Vertical angles
Two angles whose sides form two pairs of opposite rays.
242
Reflexive Property of Equality
a = a
243
Symmetric Property of Equality
If a = b, then b = a
244
Truth value
A conditional can be true or false
245
Congruent Supplements Theorem
If two angles are supplements of the same angle, then the two angles are congruent.
246
Substitution Property of Equality
If a = b! then b can replace a in any expression.
247
Complementary angles
Two angles whose measures have the sum of 90
248
Supplementary angles
Two angles whose measures have the sum of 180
249
Division Property of Equality
If a = b and c does not = 0, then a/c = b/c
250
Vertical Angles Theorem
Vertical angles are congruent.
251
Subtraction Property of Equality
If a=b, then a - c = b - c
252
Paragraph proof
A proof written as sentences in a paragraph
253
Theorem
The statement you prove true using deductive reasoning.
254
Transitive Property of Equality
If a = b and b = c, then a = c
255
Law of Syllogism
If p --> q and q --> r are true statements, then p --> r is a true statement
256
Hypothesis
The part of a conditional following "if"
257
Adjacent angles
To coplanar angles with a common side, a common vertex, and no common interior points.
258
Multiplication Property of Equality
If a = b! then a x c = b x c
259
Converse
Switches the hypothesis and conclusion of a conditional
260
Deductive reasoning
The process of reasoning logically from given statements to a conclusion.
261
Law do Detachment
If a conditional is true and its hypothesis is true, then it's conclusion is true.
262
The Distributive Property
a(b + c) = ab + ac
263
Conclusion
The part of a conditional following "then"
264
Congruent Complements Theorem
A. If two angles are complements of the same angle, then the two angles are congruent.
B. All right angles are congruent.
C. If two angles are congruent and supplementary, then each is a right angle.
265
Addition Property of Equality
If a=b, then a+c = b+c
266
Parallel planes
Planes that do not intersect
267
Parallel lines
Coplanar lines that never intersect
268
Segment
The part is a line consisting of two end points and all points between them
269
Congruent angles
Angles with the same measure
270
Perpendicular lines
Two lines that intersect to form right angles
271
Space
The set of all points
272
Acute angle
0 < x < 90
273
Angle
Two rays with a common endpoint
274
Conjecture
A conclusion you reach using inductive reasoning
275
Right angle
x = 90
276
Ray
A set of points with one endpoint and extends infinitely in the other direction
277
Angle bisector
A ray that divides an angle into two congruent coplanar angles
278
Collinear points
Points that lie on the same line
279
Straightedge
A ruler with no markings on it
280
Plane
A flat surface that has no thickness. Contains many lines and extends without end in the direction of all its lines
281
Perpendicular bisector
A line, segment, or ray that is perpendicular to a segment at its midpoint
282
Inductive reasoning
Reasoning that is based on patterns you observe
283
Obtuse angle
90 < x < 180
284
Line
A series of points that extends in two opposite directions without end
285
Opposite rays
Two collinear rays with the same endpoint
286
Straight angle
x = 180
287
Postulate or axiom
Accepted statement of fact
288
Midpoint
A point that divides a segment into two congruent segments
289
Skew lines
Noncoplanar lines that never intersect
290
Coplanar
Points and line in the same plane
291
Point
A location; has no size; represented by a small dot and is named by a capital letter.
292
Counterexample
A particular example or instance that makes a statement false
293
Congruent segments
Two segments with the same length
