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# Geometry Definitions

last edited by 11 years, 4 months ago

Acute Angle - An angle who's measure is less than 90 degrees.

Acute Triangle - A triangle with three acute angles.

Adjacent Angles - Two angles that share a common vertex, side, or ray.

Altitude of a Triangle- A perpendicular segment from a vertex that extends to the opposite side.

Angle of Depression- When you look down at an object, the angle your line of sight makes with a line drawn horizontally.

Angle of Elevation- When you look up at an object, the angle your line of sight makes with a line drawn horizontally.

Alternate exterior angles - Two angles that are formed by two lines and a transversal and lie outside the two lines and on opposite sides of the transversal.

Alternate interior angles -  Two angles that are formed by  two  lines and a transversal and lie between two lines and on opposite sides of the transversal.

Angle - Two different rays with the same endpoint.

Angle Bisector - A ray that cuts in half an angle into two angles that are congruent.

Area - The amount of surface covered by a figure.

Axiom- A rule accepted without proof, also called a postulate.

Bases of a trapezoid - the parallel sides of a trapezoid.

Base Angles of a trapezoid- pair of angles whose common side is a base of a trapezoid

Biconditional Statement- A statement that contains "if and only if".

Center of Dilation- In a dilation, it is a fixed point that a figure is enlarged or reduced with respect to it.

Centroid- The point of concurrency when it is inside the triangle.

Circle -

Circumcenter of a triangle- The point of concurry of the three perpendicular bisectors of the triangle.

Circumference - The distance around a circle.

Collinear Points - Points that are on the same line.

Complementary Angle - Two angles whose measures have the sum 90 degrees.

Concave Polygon- A polygon that is not convex.

Concurrent- Three or more lines,rays, or segments that intersect at the same point.

Conditional Statement- A type of logical statement that has two parts, a hypothesis and a conclusion.

Congruent Angles - Angles that have the same measure.

Congruent Segments - Line segments that have the same length.

Conjecture- An unproven statement based on observations.

Consecutive Interior Angles - Angles that lie between two lines and are on the same side of the transversal.

Constant - The number that you start out with in a problem.  It doesn't change.

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

Convex Polygon-  A polygon if no line contains a side.

Coordinate- The real number that corresponds to a point on a line.

Coordinate Proof- involves placing geometric figures in a coordinate plane.

Coplanar Points - Points that are on the same plane.

Corollary to a Theorem- is a statement that can be proved easily using the Corollary to the Triangle Sum Theorem.

Cosine- A trigonometric ratio, abbreviated cos. For a right triangle ABC, the cosine of the acute <A is:

Counterexample- A specific case for which the conjecture is false

Deductive Reasoning - An argument that can be formed using facts, definitions, accepted properties and the laws of logic

Defined term - Described as a point, line, segments, rays, etc.

Diagonal - a segment within a polygon that joins two vertices that do not folllow each other.

Diameter - the distance from one point of the circle to the other in which it bisects the circle.

Dilation - A transformation that stretches or shrinks a figure to create a similar figure.  A dilation is a type of similarity transformation.

Distance - The absolute value of the difference between two coordinates.

Distance from a point to a line- The length of the perpendicular segment from the point to the line.

Endpoints - Two points on the end of the line, where all points on that line lie in between the endpoints.

Equiangular - All angles in the interior of the polygon are congruent.

Equidistant- The same distants from one figure as from another figure.

Equilateral Polygon - All sides of a polygon are congruent.

Equilateral Triangle - triangle with three congruent sides.

Equivalent Statements - In general, when two statements are both true or both false, they are called equivalent statements.

Exterior Angles- angles that form linear pairs with the interior angles.  It is the angle that is outside of the polygon.

Extremes- a and d in the proportion

Geometric Mean- for two positive numbers a and b, the positive number x that satisfies . So,  and

Heptagon - A seven sided polygon

Hexagon - A six sided polygon

Hypotenuse- The side that is opposite of the right angle in a right triangle.

Hypothesis - The "if" part of a conditional statement

Incenter- The point of concurrency of the three angle bisectors of a triangle

Included Angle- The angle that is in between the two given lines or rays.

Indirect Proof- A proof in which you prove a statement is false by already assuming it's opposite is true

Inductive Reasoning - When you find a pattern in specific cases and then write a conjecture for the general case

Initial Condition - The number(s) that you start out with.  They don't change.

Interior Angles- the original angles of the polygon.

Intersection - Where two lines or planes meet

Inverse - The statement formed by negating the hypothesis and conclusion of a conditional statement.

Inverse Tangent - If tan A = x, then tan-1 x = measure of angle A.

Inverse Sine - If sin A = y, then sin-1 x = measure of angle A.

Inverse Cosine - If cos A = z, then cos-1 x = measure of angle A.

Isosceles Trapezoid- A trapezoid with congruent legs.

Isosceles Triangle- triangle with at least two congruent sides.

Kite- A quadrilateral that has 4 consecutive congruent sides, but the opposite sides arn't congruent.

Legs of a Right Triangle- The sides adjacent to the right angle.

Legs of a Trapezoid- the nonparallel sides of a trapezoid.

Line - Extends infinitely. Any two points create a line.

Line Segment -Consists of a line with two endpoints.

Linear Pair - Two adjacent angles whose noncommon sides are opposite rays.

Line Perpendicular to plane- is a line that intersects the plane in a point and forms a 90 degree angle at the exact point including the rest of the intersections.

Midpoint - A point that divides the segment into two congruent segments.

Midsegment of a Trapezoid- A segment that connects the midpoints of the legs of a trapezoid.

Midsegment of a triangle- is a segment that connects the midpoints of two sides of the triangle.

Means- b and c in the proportion

Negation- the opposite of the original statement.

n-gon - It is where n is the number of a polygon's sides.

Obtuse Angle - An angle whose measure is greater than 90 degrees.

Obtuse Triangle - triangle with one obtuse angle.

Octagon - A polygon with eight sides.

Opposite Rays - Two rays that share a common end point and point in different directions.

Orthographic projection- a two-dimensional drawing representing an object formed by the perpendicular intersections of lines

Paragraph Proof- A proof written in the form of a paragraph.

Parallelogram- A quadrilateral with both pairs of opposite sides parallel and congruent.  Its opposite angles are also congruent.

Parallel lines- Two lines in a plane that will continue forever and never intersect.

Parallel planes- Two planes that will never intersect.

Perimeter - The distance around a figure.

Perpendicular Bisector- A segment, line, or ray that is perpendicular to a segment at its midpoint.

Perpendicular Lines - Two lines that intersect to form a right angle.

Plane - Has two dimensions. Any three points that are not on the same line is a plane.

Point - Cannot be measured in any dimension, Thus that has no part. It is a dot that is like a period.

Point of Concurrency- The point of intersection of the concurrent lines,segments, or rays.

Polygon - A closed-plane figure that has 3 or more sides that do not curve.

Postulate- A rule accepted without proof.

Proof- A logical argument to show a statement is true.

Proportion- An equation that states that two ratios are equal  where a and d are the extremes and b and c are the means.

Pythagorean Triple- A set of three positive integers a, b, and c that satisfy the equation .

Quadrilateral - A four sided polygon

Ratio - A comparison of two numbers using division. The ratio of a to b, where b cannot equal 0, can be written as a to b, a : b, or as

Rate of Change - The number that is multiplied by the variable.

Ray - A line that has a beginning but no end.

Rectangle- A parallelogram with 4 right angles.

Regular - A polygon is considered regular if it is equiangular and equilateral.

Rhombus- A parallelogram with 4 congruent sides.

Right Angle - An angle who's measure is equal to 90 degrees.

Right Triangle - triangle with one right triangle.

Same-Side Interior Angles - Another name fo consecutive interior angles.

Scale Drawing -  A drawing that is the same shape as the object it represents.

Scale -  A ratio that describes how the dimensions in the drawing are related to the actual dimensions of the object.

Scale Factor - The ration of the lengths of two corresponding sides of two similar polygons

Scale Factor of Dilation -The ratio of a side length of he image of the corresponding side length of the original figure.

Scalene Triangle - triangle with no congruent sides.

Segment Bisector - A point, ray, line, line segment, or a plane that intersects the segment at its midpoint.

Sides - The rays of an angle.

Similar polygons - Two polygons that have corresponding angles that are congruent and corresponding side lengths that are proportional

Sine- A trigonometric ratio abbreviated as sin. For the right triangle ABC, the sine of the acute angle A is:

Skew lines- Lines in different planes that will never intersect.

Slope - The ratio of vertical change (rise) to horizontal change (run) between any two points of a nonvertical line.

Slope Intercept Form - The general form of a linear equation, example: y = mx + b, where m is the slope and b is the y intercept.

Solve a Right Triangle- When solving a right triangle that means you need to find the measure of all the sides and angles.

2 methods used to solve right triangles:

- Two side lengths

- One side length and the measure of one acute angle

Square- A parallelogram with 4 right angles & 4 congruent sides.

Standard Form - An equation written as Ax + By = C, where A and B are not both zero.

Straight Angle - An angle whose measure is 180 degrees.

Supplementary Angles - Two angles whose measures have a sum of 180 degrees.

Tangent- A trigonometric ratio, abbreviated as tan. For a right triangle ABC, the tangent of the acute angle A is:

Theorem- A statement which can be proven.

Transversal-  A line that intersects more than one line.

Trapezoid- A quadrilateral with one pair of parallel sides called bases and two nonparallel sides called legs.

Transitional Words - Words such as so, then, and therefore, that are used in paragraph proofs to help to make the logic clear.

Triangle - A three sided polygon

Trigonometric Ratio- A ratio of the lengths of two sides in a right triangle.

Two-Column Proof - Numbered statements and corresponding reasons that show an argument in logical order

types of slope- Positive slope (rising line), negative slope (falling line), zero slope (horizontal line), and undefined slope (vertical line).

Vertex - The endpoint of an angle.

Vertical Angles - Two angles that their sides form two pairs of opposite rays.

Volume of a solid - The number of cubic units contained in theinterior of a solid.

X - intercept - is the x - coordinate of a point where a graph crosses the x - axis.

Y - intercept - is the y - coordinate of a point where a graph crosses the y - axis.