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# GEOMETRY

### Geometry vocabulary

TermDefinition
Conjecture An unproven statement based on observations.
Inductive Reasoning The process of looking for patterns and making conjectures.
Counterexample An example that shows a conjecture is false.
Point A placeholder; it has no dimension and is usually represented by a dot.
Line A one dimensional object that extends unending; it is represented by a straight line with an arrow at each end.
Plane A two dimensional object that extends in two directions. It is usually represented by a recangular area.
Colinear Points Points that lie on the same line.
Coplanar Points Points that lie in the same plane.
Line Segment Part of a line that is represented by two end points and includes all points in between the two end points.
Ray Contains an initial (starting point) and all points on a line extending in one direction.
Opposite Rays Two rays that share the same initial point but extend in opposite directions creating a line.
Intersect Two or more geometric objects intersect if they share one or more points.
Intersection The set of points that two or more geometric objects have in common.
Postulate A rule that is accepted as truth without proof.
Coordinate A real number that corresponds to a point on a line.
Distance The absolute value of the difference between two sets of coordinates in a coordinate plane.
Length The distance between two endpoints of a line segment.
Distance Formula The function equation for finding the distance between two points in a coordinate plane.
Congruent Having equal corresponding measures.
Angle Created by two rays that have the same initial point.
Vertex The initial point (or corner) of the angle.
Congruent Angles Angles that have the same measure.
Measure of an Angle The sides of the angle can be matched one-to-one with real numbers from 0-180. The measure is the absolute value of the difference between those real numbers.
Interior of an Angle All points that lie between the two ray sides of the angle.
Exterior of an Angle All points that lie outside of the two ray sides of the angle.
Acute Angle An angle that measures less than 90 degrees.
Obtuse Angle An angle that measures more than 90 degrees but less than 180 degrees.
Straight Angle An angle that measures 180 degrees forming a straight line.
Right Angle An angle that measures exactly 90 degrees.
Adjacent Angles Two angles that share a common vertex and a common side but do not have any common interior points.
Midpoint Divides or bisects a line segment into two congruent segments
Bisect To divide a line segment or angle into two congruent parts.
Segment Bisector A segment, ray, line, or plane that intersects a line segment at its midpoint.
Compass A construction tool used to create arcs and circles.
Straight Edge A tool used to draw straight lines such as a ruler.
Construct To draw using a limited set of tools such as a straight edge and a compass.
Construction A drawing using a limited set of tools.
Midpoint Formula An algebraic function using two ordered pairs on a coordinate plane to find the midpoint of a line segment.
Angle Bisector A ray that that divides an angle into two adjacent congruent angles
Vertical Angles Congruent angles created by intersecting lines. They share the same vertex and their sides are formed by two pairs of opposite rays.
Linear Pair Two adjacent angles whose non-common sides are opposite rays (they form a line), and whose measures add to 180 degrees.
Complementary Angles Two angles whose measures add to 90 degrees.
Supplementary Angles Two angles whose measures add to 180 degrees.
Complement The angle whose measure added to a given angle is 90 degrees.
Supplement The angle whose measure added to a given angle is 180 degrees.
Conditional Statement A logical statement that has two parts, a hypothesis and a conclusion.
If-Then Statement A conditional statement that uses "If" with the hypothesis and "Then" with the conclusion.
Hypothesis The beginning or introduction to a condition.
Conclusion The closing of a conditional statement based on the results of the given hypothesis.
Converse The result of switching the hypothesis and conclusion phrases in a conditional statement.
Negation Writing the negative of a conditional statement.
Inverse Statement The result of writing the negation of a conditional statement.
Contrapositive The result of switching the hypothesis and conclusion of a negation or inverse conditional statement.
Equivalent Statements Two conditional statements that are either both true, or both false.
Perpendicular Lines Two lines that intersect forming right angles at their intersection.
Biconditional Statement A statement containing the phrase "If and only if."
Logical Arguement An argument based on deductive reasoning that uses facts, definitions, and accepted properties in a logical order.
Symbolic Notation Uses symbols to stress a given order of the hypothesis, conclusion, or negation of a conditional statement.
Reflexive Property Equal to itself.
Symmetric Property A reverse image of a statement or writing an equation or expression in reverse order.
Theorem A true statement using a reason that has been previously proven.
Two-Column Proof A proof using "Statements" as one column and "Reasons" as the other column with a numbered progression in a logical order.
Paragraph Proof A proof written in logical order with the progression in complete sentence form.
Parallel Lines Two lines that lie in the same plane but do not intersect.
Skew Lines Two lines that do not intersect but that lie in different planes.
Parallel Planes Two planes that do not intersect.
Transversal A line that intersects two or more coplanar lines at different intersection points.
Corresponding Angles Two angles on the same side of a transversal that sit in the same place on two different lines.
Alternate Exterior Angles Two angles on opposite sides of a transversal but on the outside of the two lines.
Alternate Interior Angles Two angles on opposite sides of a transversal but in between the two lines.
Consecutive Interior Angles Two angles on the same side of a transversal and in between the two lines (also known as Same-side Interior angles).
Triangle A figure formed by three segments joining three non-collinear points.
Legs In a right triangle they are the sides adjacent to the right angle; in an isosceles triangle, they are the congruent sides.
Hypotenuse The side opposite the right angle, or the longest side of a right triangle.
Base In an isosceles triangle, it is the non-congruent third side.
Interior Angles The three vertices of a triangle whose measures add to 180 degrees.
Exterior Angles When the sides of a triangle are extended, they are the three angles adjacent to the interior angles; supplementary to the interior angles of a triangle.
Corollary A statement that can be proven by using a theorem; an addition to a theorem.
Equilateral A triangle that has three congruent sides.
Equiangular A triangle that has three congruent angles.
Scalene A triangle that has no congruent sides.
Isosceles A triangle that has at least two congruent sides.
Equidistant Being equally distant from two or more points or objects.
Concurrent Two or more lines having the same intersection point.
Circumcenter The center of a circle circumscribed about a triangle.
Incenter The center of a circle inscribed in a triangle.
Median of a Triangle The segment connecting the midpoint of a side to the opposite vertex.
Centroid of a Triangle The point of concurrency f the medians of a triangle.
Altitude of a Triangle The perpendicular height of a triangle from a side to the opposite vertex.
Orthocenter The point of concurrency of the altitudes of a triangle.
Ratio Comparing two objects with the same unit of measure in (:) or fraction form.
Proportion Two equivalent ratios.
Means The divisor of the first ratio compared to the numerator of the second ratio.
Extremes The numerator of the first ratio compared to the divisor of the second ratio.
Geometric Mean The square root of the product of the means in a proportion.
Similar Polygons Objects such that their corresponding angles are congruent, and their corresponding sides are proportional.
Scale Factor The smallest form of the proportional ratio comparing two similar polygons.
Circle In a plane, the set of all points equadistant from a center point.
Radius The distance from the center of a circle to the circle.
Congruent Circles Circles having the same radius measure.
Diameter The distance across a circle through its center, or the chord of a circle that includes the center.
Chord A segment whose endpoints are on the circle.
Secant A line that intersects a circle in two points.
Tangent A line that intersects a circle in exactly one point.
Tangent Circles Circles that intersect at exactly one point.
Concentric Circles Coplanar circles that have a common center.
Common Tangent A line that is tangent to two or more circles.
Interior of a circle The set of all coplanar points on the inside of a circle.
Exterior of a circle. The set of all coplanar points on the outside of a circle.
Point of Tangency The exact point at which a line or circle intersects a circle.
Central Angle An angle whose vertex is the center of a circle.
Minor Arc Part of a circle that measures less than 180 degrees.
Major Arc Part of a circle that measures more than 180 degrees.
Semicircle An arc whose endpoints are the endpoints of the diameter of a circle, or half of a circle in degrees.
Measure of a Minor Arc The measure of the acute central angle.
Measure of a Major Arc The difference between 360 degrees and the measure of the associated minor arc.
Congruent Arcs Two arcs of the same or congruent circles that have the same measure.
Created by: mboothe