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Geometry Definitions

Page history last edited by Venesa 14 years, 3 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 Formula


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


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 Formula


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 Formula 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 Formula.


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 Formula 


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:

Formula   Formula


 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.


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