HONORS GEOMETRY VOCABULARY WORDS

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 :

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.

• Radius segment whose endpoints are the center of the circle and a point on the circle.
• Chord segment that connects two points on the circle.
• Diameter chord that passes through the center of the circle.
• Secant line that intersects a circle in two points.
• Tangent line in the plane of the circle that intersects the circle in one point.

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.

• Congruent arcs – arcs with equal measure in the same circle or in congruent circles.
• Inscribed angles – angle whose vertex is on the circle and whose sides are chords 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.