Definition of point :
has no size; length, width, or height. It is represented by a dot and named by a capital letter.
Definition of Line :
Set of points which has infinite length but no width or height. A line is named by a lower case letter or by any two points on the line.
Definition of Plane :
Set of points that has infinite length and width but no height. We name a plane with a capital ‘funny font’ letter.
Definition of Collinear points :
Points that lie on the same line.
Definition of noncollinear points :
Points that do not lie on the same line.
Here A and B are colinear points. C, D and E are non collinear points.
Definition of coplanar points :
Points that lie on the same plane.
Definition of noncoplanar points :
Points that do not lie on the same plane.
Definition of Segment :
Part of a line that consists of two points called endpoints and all points between them.
Definition of Ray :
Ray- is the part of a line that contains an endpoint and all points extending in the other direction.
Definition of Congruent segments :
Segments that have the same length.
Definition of bisector of a segment :
Line, ray segment, or plane that divides a segment into two congruent segments.
Definition of Midpoint of a segment :
A point that divides the segment into two congruent segments.
Definition of Acute angle :
Angle whose measure is between 0 degrees and 90 degrees.
Definition of Right angle :
Angle whose measure is 90 degrees.
Definition of Obtuse angle :
Angle whose measure is greater than 90 degrees but less than 180 degrees.
Definition of Straight angle :
Angle whose measure is 180 degrees.
Definition of Congruent angles :
Angles that have the same measure.
Definition of Angle bisector :
Ray that divides an angle into two congruent adjacent angles.
Definition of Triangle :
The figure formed by three segments joining three noncollinear points. Each of the three points
is a vertex of the triangle and the segments are the sides.
Definition of Adjacent angles :
Two coplanar angles with a common vertex and a common side between them.
Definition of Vertical angles :
The non-adjacent angles formed by two intersecting lines.
Definition of Complementary angles :
Two angles whose sum is 90 degrees.
Definition of Supplementary angles :
Two angles whose sum is 180 degrees.
Definition of Perpendicular lines :
Two lines that intersect to form right angles.
Definition of parallel lines :
Two lines are parallel if they are coplanar and do not intersect.
Definition of Skew lines :
They are noncoplanar lines they will not intersect.
Definition of polygon :
Polygon |
Not a polygon |
The union of 3 or more coplanar segments that meet only at endpoints such that at most two segments meet at one endpoint and each segment meets exactly two other segments.
Definition of Regular polygon :
A polygon which is equilateral and equiangular.
Congruent triangles two triangles are congruent if corresponding sides are congruent and corresponding angles are congruent.
Definition of Median of a triangle :
A segment from the vertex of a triangle to the midpoint of the opposite side.
Altitude of a triangle :
The segment from the vertex of a triangle perpendicular to the line containing the opposite side.
Definition of Parallelogram :
A quadrilateral with both pairs of opposite sides parallel.
Definition of rectangle :
Rectangle parallelogram with a right angle.
Definition of Rhombus :
Parallelogram with consecutive sides congruent.
Definition of Square :
All sides congruent and all four right angles.
Trapezoid quadrilateral with exactly one pair of opposite sides parallel.
Definition of Ratio :
The comparison of two numbers by division.
Definition of Proportion :
Equation that states two ratios are equal.
Definition of Pythagorean Theorem :
In a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse
Definition of circle :
Circle the set of points in a plane that are equidistant from a fixed point called the center.
Definition of concentric circles :
Concentric circles – two or more circles in the same plane with the same center.
Congruent circles – circles that have congruent radii.
Definition of sphere :
Sphere set of points in space a given distance from a given point called the center.
Definition of arc :
Arc consists of two points and the continuous part of a circle between them.
CD is the arc.
Definition of semicircle :
Semi-circle arc whose endpoints are the endpoints of a diameter.
Minor arc – arc whose measure is less than a semi-circle (180 degree).
Major arc – arc whose measure is greater than a semi-circle (180 degrees).
Definition of central angle :
Angle whose vertex is the center of the circle and whose rays are radii of the circle.
Definition of Hypothesis :
Hypothesis in a conditional statement the statement that immediately follows the word ‘if’.
Definition of conclusion :
Conclusion – in a conditional statement the statement that immediately follows the word ‘then’.
Definition of converse :
Converse – the statement formed by exchanging the hypothesis and the conclusion of a conditional statement.
Definition of inverse :
Inverse – the statement formed by negating both the hypothesis and the conclusion of a conditional statement.
Definition of contrapositive :
Contrapositive – the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.
Definition of bi conditional :
Bi-conditional – the conjunction of a conditional statement and its converse.
Deductive reasoning – a system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions.
Inductive reasoning :
Inductive reasoning – reasoning that uses a number of specific examples to arrive at a plausible prediction.
Definition of proof :
Proof – a logical argument in which each statement you make is supported by a statement that is accepted as true.
Definition of postulate :
Postulate- a statement that describes a fundamental relationship between basic terms of geometry. Postulates are accepted as true without proof.
Definition of theorem :
Theorems – a statement or conjecture that can be proven true by given, definitions, postulates, or already proven theorems.
Definition of two column proof :
Two-column proof – a formal proof that contains statements and reasons organized in two columns.
Paragraph proof – an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true.
Definition of flow proof :
Flow proof – a proof that organizes statements in logical order, starting with given statements. Each statement is written in a box with the reason verifying the statement written below the box.
Definition of conjecture :
Conjecture – an educated guess based on known information.
Definition of sine :
Sine – for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the hypotenuse.
Definition of cosine :
Cosine – for an acute angle of a right triangle, the ratio of the measure of the leg adjacent to the acute angle to the measure of the hypotenuse.
Definition of tangent :
Tangent – for an acute angle of a right triangle, the ratio of the measure of the leg opposite the acute angle to the measure of the leg adjacent to the acute angle.
Definition of space :
Space – set of all points.
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