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# GEOMETRY

### Geometry vocabulary

Term | Definition |
---|---|

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. |