100 Word Vocabulary List Geometry

Geometry - branch of mathematics that deals with points, lines, planes and solids and examines their properties.

Point – has no size; length, width, or height.  It is represented by a dot and named by a capital letter.

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.

Plane – set of points that has infinite length and width but no height. We name a plane with a capital letter.

Space – set of all points.

Collinear points – points that lie on the same line.

Noncollinear points – points that do not lie on the same line.

Coplanar points – points that lie on the same plane.

Noncoplanar points – points that do not lie on the same plane.

Segment – part of a line that consists of two points called endpoints and all points between them.

Ray- is the part of a line that contains an endpoint and all points extending in the other direction.

Congruent segments – segments that have the same length.

Bisector of a segment – line, ray segment, or plane that divides a segment into two congruent segments.

Midpoint of a segment – a point that divides the segment into two congruent segments.

Acute angle – angle whose measure is between 0 degrees and 90 degrees.

Right angle – angle whose measure is 90 degrees.

Obtuse angle – angle whose measure is greater than 90 degrees but less than 180 degrees.

Straight angle – angle whose measure is 180 degrees.

Congruent angles – angles that have the same measure.

Angle bisector – ray that divides an angle into two congruent adjacent angles.

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.

Acute triangle- triangle that has all acute angles.

Right triangle – triangle with a right angle.

Obtuse triangle – triangle with an obtuse angle.

Equiangular triangle – triangle with all angles congruent.

Scalene triangle – triangle with no sides congruent.

Isosceles triangle – triangle with at least two sides congruent.

Equilateral triangle – triangle with all sides congruent.

Adjacent angles – two coplanar angles with a common vertex and a common side between them

Vertical angles – the non-adjacent angles formed by two intersecting lines.

Complementary angles – two angles whose sum is 90 degrees.

Supplementary angles – two angles whose sum is 180 degrees.

Perpendicular lines – two lines that intersect to form right angles.

Parallel lines – two lines are parallel if they are coplanar and do not intersect.

Skew lines – are noncoplanar lines they will not intersect.

Polygon – 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.

Regular polygon – polygon which is equilateral and equiangular.

Congruent triangles – two triangles are congruent if corresponding sides are congruent and corresponding angles are congruent.

Median of a triangle – segment from the vertex of a triangle to the midpoint of the opposite side.

Altitude of a triangle – segment from the vertex of a triangle perpendicular to the line containing the opposite side.

Parallelogram – quadrilateral with both pairs of opposite sides parallel.

Rectangle – parallelogram with a right angle.

Rhombus – parallelogram with consecutive sides congruent.

Square – all sides congruent and all four right angles.

Trapezoid – quadrilateral with exactly one pair of opposite sides parallel.

Ratio – comparison of two numbers by division.

Proportion – equation that states two ratios are equal.

Pythagorean Theorem – in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse

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.

Concentric circles – two or more circles in the same plane with the same center.

Congruent circles – circles that have congruent radii.

Sphere – set of points in space a given distance from a given point called the center.

Arc – consists of two points and the continuous part of a circle between them.

Semi-circle – arc whose endpoints are the endpoints of a diameter.

Minor arc – arc whose measure is less than a semi-circle or 180 degree.

Major arc – arc whose measure is greater than a semi-circle or 180 degrees.

Central angle of a circle – 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.

Bases – congruent polygons lying in parallel planes.

Altitude – segment joining the two base planes and perpendicular to both.

Lateral faces – faces of a prism that are not its bases.

Lateral edges – intersection of adjacent lateral faces form lateral edges.

Lateral area – sum of the area of its lateral faces.

Surface area – sum of the area of all its faces.

Volume – number of cubic units contained in a solid.

 Right Prism – is a prism whose lateral faces are rectangles.

 Oblique prism – is a prism whose lateral faces are parallelograms.

Cube – is a prism where all sides are squares.

Triangular prism – is a prism whose parallel faces (the bases) are congruent triangles.

Cylinder – has two congruent circular bases in parallel planes.

Cone – has a vertex and a circular base.

Line of symmetry – divides a figure into two congruent halves that reflect each other.

Perimeter – of a polygon is the distance around the polygon.

Area – of any surface is the number of square units required to cover the surface.

Volume – of a 3-dimensional figure is the number of cubic units contained in the solid.

Circumference – the distance around a circle.

Conditional statement – a statement that can be written in an if-then form.

Hypothesis – in a conditional statement the statement that immediately follows the word if.

Conclusion – in a conditional statement the statement that immediately follows the word then.

Converse – the statement formed by exchanging the hypothesis and the conclusion of a conditional statement.

Inverse – the statement formed by negating both the hypothesis and the conclusion of a conditional statement.

Contrapositive – the statement formed by negating both the hypothesis and conclusion of the converse of a conditional statement.

Biconditional – 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 – reasoning that uses a number of specific examples to arrive at a plausible prediction.

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

Postulate- a statement that describes a fundamental relationship between basic terms of geometry. Postulates are accepted as true without proof.

Theorems – a statement or conjecture that can be proven true by given, definitions, postulates, or already proven theorems.

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.

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.

Conjecture – an educated guess based on known information.

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 the acute angle to the measure of the leg adjacent to the acute angle.