Geometry Vocabulary

Midpoint  The point halfway between the endpoints of a segment. i.e. If C in the midpoint of segment AB, i.e. If C in the midpoint of segment AB, then AC=CB then AC=CB

Angle Bisector A Ray that divides an angle into 2 congruent angles.

Adjacent Angles  2 angles that lie on the same plane, have a common vertex, a common side, but no common interior points

Vertical Angles  2 nonadjacent angles formed by 2 intersecting lines

Linear Pair  A pair of adjacent angles whose noncommon sides are opposite rays

Complementary Angles  2 angles whose measures have a sum of 90 degrees.

Supplementary Angles  2 angles whose measures have a sum of 180 degrees.

Perpendicular  Lines that intersect to form right angles.

Conjecture  An educated guess based on known information

Inductive Reasoning  Examining several specific examples or situations to arrive at a conjecture.

Counterexample  A false example used to demonstrate that a conjecture is false.

Conditional Statement  Any statement that can be written in if – then form.

Hypothesis  The phrase immediately following the word if in a conditional statement.

Conclusion  The phrase immediately following the then in a conditional statement.

Converse  A conditional statement in which the hypothesis and conclusion are interchanged.

Deductive Reasoning  A form of reasoning in which one uses facts, rules, definitions, properties, postulates, and or theorems to reach a valid conclusion.

Postulate (axiom)  A statement that describes a fundamental relationship between the basic terms in geometry. All postulates are statements that are accepted as true.

Theorem  A statement that must be proved in order to be accepted as true.

Proof  A logical argument in which each statement you make is supported by a statement that is accepted as true.

Parallel Lines  Coplanar lines that never intersect

Skew Lines  Lines that do NOT intersect and are NOT coplanar.

Transversal  A line that intersects two or more lines in a plane at different points.

Right Triangle  A triangle with one right angle

Scalene Triangle  A triangle in which no 2 sides are congruent

Isosceles Triangle  A triangle in which at least 2 sides are congruent

Included Angle  The angle between 2 adjacent sides

Included Side  A side of a polygon that is between 2 adjacent angles

Corollary  A statement that can be easily proved using a theorem

Remote Interior Angles  The interior angles of a triangle that are not adjacent to a given exterior angle.

Congruent Triangles (CPCTC)  Triangles that are the same size and same shape. All corresponding parts are congruent.

Perpendicular Bisector  A line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side

Point of Concurrency  The point of intersection when 3 or more lines intersect at a common point.

Circumcenter  The point of concurrency of the perpendicular bisectors of a triangle.

Median  A segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex.

Incenter  The point of concurrency of the angle bisectors of a triangle.

Centroid  The point of concurrency for the medians of a triangle.

Altitude  A segment from a vertex to the line containing the opposite side and is perpendicular to the line containing that side.

Orthocenter  The intersection of the altitudes of a triangle.

Indirect Reasoning  Reasoning in which you begin by assuming the conclusion is false and then show that this assumption leads to a contradiction of the hypothesis, or some accepted fact, definition, or theorem.

Ratio  A comparison of two quantities.

Similar Polygons  A numerical ratio that compares the lengths of corresponding sides of similar figures.

Scale Factor  Polygons that have the same shape but may be different sizes. Their corresponding angles are congruent and the measures of their corresponding sides are proportional.

Midsegment  A segment in a triangle whose endpoints are the midpoints of 2 sides of the triangle.

Trigonometry  The study of the properties of triangles and trigonometric functions and their applications.

Trigonometric Ratios  A ratio of the lengths of sides of a right triangle.

Trigonometric Identity  An equation involving a trigonometric ratio that is true for all values of the angle measure.

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.

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.

Tangent  For an acute angle of a right triangle, the ratio of the measure of the leg opposite to the acute angle to the measure of the side adjacent to the acute angle.

Arc  A part of a circle that is defined by two endpoints.

Circle  A locus of points in a plane equidistant from a given point.

Chord  A segment with endpoints on a circle.

Circumference  The distance around a circle.

Concentric Circles  Circles that share the same center point but have different radii.

Major Arc  An arc with a measure greater than 180 degrees.

Central Angle  An angle that intersects a circle in two points and has a vertex at the center of the circle.

Minor Arc  An arc with a measure less than 180 degrees and greater that zero.

Semicircle  An arc that measures 180 degrees.

Diameter  A chord that passes through the center of the circle.

Apothem  A segment that is drawn from the center of a regular polygon perpendicular to a side of the polygon.

Great Circle  For a given sphere, the intersection of the sphere and a plane that contains the center of the sphere.

Lateral Area  For prisms, pyramids, cylinders, and cones the area of the figure, not including the bases.

Net  A two-dimensional figure that when folded forms the surfaces of a three- dimensional object.

Polyhedron  A closed three-dimensional figure made up of flat polygonal regions.

Right Cone  A cone with an axis that is also an altitude.

Transformations  In a plane, a mapping for which each point has exactly one image point and each image point has exactly one pre- image point.

Volume  A measure of the amount of space enclosed by a three-dimensional figure.