Geometry Vocabulary Flashcards
8th Grade (TCMS)
1
Q
An angle measuring exactly 90 degrees.
A
Right Angle
2
Q
Lines that intersect at right angles.
A
Perpendicular Lines
3
Q
Lines that do not intersect and are not parallel.
A
Skew Lines
4
Q
An angle measuring exactly 180 degrees.
A
Straight Angle
5
Q
An exact statement, written formally, of the meaning or description of a word.
A
Definition
6
Q
A transformation that produces the mirror image of a geometric figure.
A
Reflection
Accros a line of reflection
7
Q
A transformation of a figure by turning it about a center point or axis.
A
Rotation
The amount of rotation can be expressed in the number of degrees. The direction of the rotation for two-dimensional figures can be expressed as clockwise or counterclockwise.
8
Q
A transformation in which every point in a figure is moved in the same direction and by the same distance.
A
Translation
9
Q
A transformation that preserves distance and angle measure.
A
Isometry
10
Q
A transformation of points in space consisting of a sequence of one or more translations, reflections, or rotations.
A
Rigid Transformation/Rigid Motion
Rigid transformations preserve distances and angle measures (congruency).
11
Q
Figures having exactly the same shape and size. One can be mapped to the other using a rigid transformation(s).
A
Definition of Congruence in terms of Rigid Motions
12
Q
A standardized form of showing a transformation.
A
Mapping
13
Q
Corresponding points have the same distance from a line.
A
Line of reflection
14
Q
A proportional increase or decrease in size in all directions.
A
Dilation
15
Q
To separate or divide.
A
Partition
16
Q
The constant that is multiplied by the length of each side of a figure to produce an image that is the same shape as the original figure.
A
Scale Factor
17
Q
Divides a line segment into two equal (congruent) segments.
A
Midpoint
18
Q
Having exactly the same shape but not necessarily the same size. 1 figure can be obtained by a dilation.
One figure can be obtained from the other by a dilation or a sequence of transformations that includes a dilation.
A
Similarity/Similar
19
Q
An arrangement of shapes closely fitted together in a repeated pattern without gaps or overlaps.
A
Tessellation
20
Q
The points of a line can be placed in a one-to-one correspondence with the real numbers such that the distance between two distinct points is the absolute value of the difference of the corresponding real numbers.
A
Ruler Postulate
21
Q
Points on the same line.
A
Collinear Points
22
Q
If points A, X, and B are collinear points and point X is between points A and B, then AX+XB=AB.
A
Segment Addition Postulate
23
Q
If point X is in the interior of angle AMB, then measure of angle AMX+ the measure of angle XMB= the measure of angle AMB.
A
Angle Addition Postulate
24
Q
A line, ray, or line segment that cuts a line segment into two equal parts.
A
Segment Bisector
25
A triangle containing an interior right angle.
Right Triangle
26
Contains at least two equal length sides and two equal interior angle measures.
Isosceles Triangle
27
A line, ray , or line segment that cuts an angle into two equal parts.
Angle Bisector
28
Emphasizes using facts, ideas, and assumptions.
Euclidean Geometry
29
An idea that is assumed to be true or something that is self-evident.
Postulate
30
An idea that has to be shown to be true through a chain of reasoning, often called a proof.
Theorem
31
If two lines intersect, then vertical angles are congruent.
Vertical Angles Theorem
32
A mathematical statement that has not yet been proven.
Conjecture
33
Uses facts and general principles to draw conclusions.
Deductive Reasoning
34
Uses specific observations and patterns to draw conclusions.
Inductive Reasoning
35
A statement that disproves a conjecture.
Counterexample
36
1. Infinite length, no height and no width.
2. Assumed to be straight.
3. Considered one-dimensional.
4. Considered an undefined term.
5. Goes on forever in both directions.
Facts about lines
37
1. Infinite length and width, with no height
2. Considered two-dimensional.
3. Considered an undefined term.
4. Goes on forever.
Facts about Planes
38
1. No length, no width, and no height.
2. Named by an ordered pair in the coordinate plane.
3. Indicates a location or position.
4. No dimension or actual size.
Facts about Points
39
A term which when explaining the term, the explanation relies on the term itself or a close synonym.
Undefined Term
40
A portion or piece of a line. Its length is infinite and is determined by its two endpoints.
Line Segment
41
Same distance or same length.
Equidistant
42
Known as "Father of Geometry".
Euclid
43
If two figures have equal measurements, then the figures are congruent, and vice-versa.
Definition of Congruence
44
A statement in the format of "if p, then q". The phrase P is the hypothesis, and the phrase q is the conclusion.
Conditional Statement
45
A statement in which the given conditional "if p, then q" changes to "if q, then p".
Converse Statement
46
A statement in which the given conditional "if p, then q" changes to "if not p, then not q."
Inverse Statement
47
A statement in which the given conditional "if p, then q" changes to "if not q, then not p"
Contrapositive Statement
48
A statement written in the format "if and only if" and can only be qualified as this when both the conditional and the converse statement are BOTH true.
Biconditional Statement
49
a diagram representing mathematical or logical sets pictorially as circles. Common elements of the sets are within the overlap of the circles.
Venn Diagram
50
The opposite of a statement.
Negation
51
Two angles that have a common length between them.
Linear Pair
52
A whole number greater than 1 that has at least one whole number factor other than one and itself.
Composite Number
53
A whole number greater than 1 that is not divisible by any whole number other than 1 and itself.
Prime Number
54
Two angles whose measures sum to 90 degrees.
Complementary Angles
55
Complements of congruent angles are congruent.
Congruent Complements Theorem
56
A true statement that is a simple deduction from a theorem or postulate. Its proof requires only a few simple statements in addition to the proof of the original theorem or postulate.
Corollary
57
Complements of the same angle are congruent.
Corollary to Congruent Complements Theorem
58
Two angles whose measures sum is exactly 180 degrees.
Supplementary Angles
59
Supplements of congruent angles are congruent.
Congruent Supplements Theorem
60
Supplements of the same angle are congruent.
Corollary to Congruent Supplements Theorem.
61
Two adjacent angles formed by two intersecting lines.
Linear Pair
62
If two angles form a linear pair, then they are supplementary.
Linear Pair Postulate
63
Are the opposite angles formed when two lines intersect.
Vertical Angles
64
If two lines intersect, then vertical angles are congruent.
Vertical Angles Theorem
65
Line that intersects two or more lines in the same plane at different points.
Transversal
66
Are angles that are in the same position on two parallel lines in relation to a transversal.
Corresponding Angles
67
If two parallel lines are intersected by a transversal, then corresponding angles are congruent.
Corresponding Angles Theorem
68
If two parallel lines are intersected by a transversal, then alternate exterior angles are congruent.
Alternate Exterior Angles Theorem
69
If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
Alternate Interior Angles Theorem
70
If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are supplementary.
Consecutive Interior Angles Theorem
71
If two parallel lines are intersected by a transversal, then exterior angles on the same side of the transversal are supplementary.
Consecutive Exterior Angles Theorem
72
When two or more transformations are combined.
Sequence of Transformations
## Footnote
Also called Composition of Transformations.
73
One-to-one correspondence between two sets of points.
Transformation
74
Two figures are congruent if and only if there exits one or more rigid motions, which will map one figure onto the other.
Definition of Congruence in Terms of Rigid Motions.
75
Two triangles are congruent if the three sides of one are congruent to the three sides of the other, respectively.
Side-Side-Side (SSS) Congruence Postulate
76
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, respectively, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence Postulate
77
If two angles and an included side of one triangle are congruent respectively to two angles and an included side of a second triangle, then the two triangles are congruent.
Angle-Side- Angle (ASA) Congruence Theorem
78
If two angles and a side opposite one of them are congruent to two angles and the corresponding side of the other, respectively, then the triangles are congruent.
Angle-Angle-Side (AAS) Congruence Theorem
79
Two right triangles are congruent if the hypotenuse and a leg of one are congruent to the hypotenuse and a leg of the other, respectively.
The Hypotenuse-Leg (HL) Theorem
80
If two triangles are congruent, then all corresponding parts of the triangles are congruent.
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
81
If two polygons are congruent, then all corresponding parts of the polygons are congruent.
Corresponding Parts of Congruent Polygons are Congruent
82
If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Angle-Angle Similarity (AA) Theorem
83
If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
Side-Side-Side Similarity (SSS) Theorem
84
If the lengths of two sides are proportional and their included angles are congruent on two different triangles, then the triangles are similar.
Side-Angle-Side Similarity (SAS) Theorem
85
Opposite/Hypotenuse
Sine (0)
86
Adjacent/Hypotenuse
Cosine (0)
87
Opposite/Adjacent
Tangent (0)
88
A quadrilateral containing two pairs of parallel sides.
Parallelogram
89
A quadrilateral that contains four right angles. May be oblong or square.
Rectangle
90
A quadrilateral with 4 right angles and 4 equal side lengths
Square
91
A quadrilateral containing four equal side lengths.
Rhombus
92
A quadrilateral containing 4 equal-length sides.
Rhombus
93
A quadrilateral with exactly two pairs of adjacent congruent sides.
Kite
94
A quadrilateral with at least one pair of parallel sides.
Trapezoid
95
A trapezoid with congruent base angles.
Isosceles Trapezoid
96
Part of a trapezoid that connects the non-parallel sides at their midpoint. Sometimes referred to as the midsegment.
Median
97
Part of a trapezoid is any segment from a point on one of the bases perpendicular to the line containing the other base.
Altitude
98
If every plane parallel to the two bases of two solids results in cross sections of equal area and the two solids have congruent altitudes then the solids have equal volumes.
Cavalieri's Principle for 3-d Solids
99
The distance from the base to the apex along a lateral face
Slant height
100
The perpendicular distance from the apex to the base.
Vertical Height or Altitude
101
A 3-D figure with a circular base and an apex that is connected to the base by a collection of line segments that form a curved surface.
Cone
102
A figure with a polygonal base and triangular faces. The triangular faces have the same size and shape and they connect the sides of the base to a common point called the apex.
Pyramid
103
A 3-D figure, where all points are equidistance from a point called the center.
Sphere
104
Sum of the area of the figure's face.
Lateral Area
105
The sum of the lateral area of the figure's faces and the area of the figure's bases.
Surface Area
106
An angle with its vertex at the center of the circle with a radius as its side.
Central Angle
107
A line segment on the interior of a circle with both endpoints lying on the circle.
Chord
108
An angle which is formed in the interior of a circle when two chords share an endpoint.
Inscribed Angle
109
The measure of an inscribed angle is one-half the measure of the intercepted arc.
Inscribed Angle Theorem
110
A line or line segment that passes through two points on a circle. In the interior of the circle, this forms a chord.
Secant
111
The measure of the angle formed by two secants intersecting in the exterior of a circle is one-half the difference of the measures of the intercepted arcs.
Exterior Secant Angle Theorem
112
A line or segment that intersects a circle at exactly one point.
Tangent
113
A polygon which has all of its vertices on a circle.
Inscribed Polygon (in a circle)
114
The smallest circle that includes a plane figure. If the figure is a polygon, then the circle must contain all of the vertices of the polygon.
Circumscribed Circle
115
The point where three or more lines intersect.
Point of concurrency
116
Point of concurrency of the perpendicular bisectors of a triangle.
Circumcenter
## Footnote
The center of a triangle's circumscribed circle
117
Point of concurrency of the angle bisectors of a triangle.
Incenter
