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