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.