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An All Inclusive A to Z Guide to Geometry

written by: Kathy Foust • edited by: SForsyth • updated: 1/5/2012

To know every geometry definition a to z, one first has to know geometry concepts. Use this guide to understand basic concepts so that the more specific ones will be easy to comprehend.

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    How to Combine Terms

    The first thing to understand is that the basic terms all combine to make more specific terms. Consider the following concept: Acute Alternate Interior Angles. This seems like a long and difficult term at first glance, but once you take the term apart and look at how the terms combine together, it's really very simple.

    Acute means something that is "sharp or sudden". If you consider how an acute angle looks, you will see that this is an apt description of the outside of the acute angle. There is a sharp point at the end. "Acute" in geometry describes an angle that measures less than 90 degrees, or is smaller than a "right angle".

    Alternate means "every other one of a series". In geometry, alternate angles are those that are follow an "every other one" sequence within a set of angles.

    Interior means "inside". In geometry, the term "interior" refers to the placement of the term in question. For instance, "interior angles" would mean "inside angles".

    Angles are understood to be an area described by two intersecting lines. The lines and points of intersection are described when the angle is named.

    In this example, if we were looking for Acute Alternate Interior Angles, we would see we are looking for Angles that are smaller than 90 degrees, create a pattern of "every other one", are found on the inside of a plane that has more than four angles (because they are "inside of something", which cannot be created with only two lines). Notice how the terms were used together to create a more specific concepts. Use the terms listed below to understand how you can form specific concepts.

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    Basic Concepts

    Know every geometry definition a to z by putting together simple geometry concepts. Review the terms below and place them in concepts that are easily understood by you. For instance, you can remember the term "acute" based on your own interests. Remember "acute" is "sharp" or an "angle that measures less than 90 degrees". Based on your interests, remember "acute" by remembering that "A cute" girl can make you turn your head sharply or that the finer the angle, the sharper or more "acute" the point.

    Acute: Measuring less than 90 degrees.

    Adjacent: Has a common side and vertex, but no common interior points. Hence adjacent angles may be next to each other, but not inside of each other.

    Angle: The area created by the meeting of two lines or rays.

    Arc: A segment of a circle.

    Area: The measure of the interior space of any polygon.

    Axis: Lines that define horizontal and vertical placement, such as the x-axis and y-axis.

    Base: The foundation. For instance, this can be remembered by imagining the bases of a trapezoid. These are the parallel sides of any trapezoid. A building that forms the shape of a trapezoid will have the "bases" as the foundation and roof of the building.

    Biconditional: Having two "conditions" or rules.

    Center: The midpoint, "equidistant from all extremities".

    Circumference: The limit of any perimeter. Measured in a straight line through a center point from opposing sides.

    Collinear: On the same line.

    Complimentary: Equally 90 degrees. Two angles compliment each other if they form 90 degrees when added together.

    Concave: Curved inward. (Think "cave"). The opposite of convex.

    Congruent: Having the same measurement.

    Consecutive: One following the other.

    Convex: Curved outward.

    Degree: Unit of measure describing an angle in geometry.

    Diameter: Line containing the center of the circle and going from opposing ends of the circle

    Equi: Terms that start with "Equi" tend to mean "equal" and even "congruent".

    Exterior: On the outside. The opposite of interior.

    Hypotenuse: The side opposite the right angle in a right triangle.

    Hypothesis: An idea that meets conditions.

    Intersect: Having points in common.

    Inverse: Negating something else.

    Isometry: When an image and preimage (simply put, two shapes that are mirrors of each other) are congruent of each other.

    Lateral: "To the side". For instance, in a prism faces that are not bases are called lateral faces.

    Line: Represented by double arrows, the line can go on indefinitely in either direction.

    Symmetry: Causes a reflection of a plane.

    Mid or median: These terms designate use of the center of something, the "something" being defined by the term following "median" or "mid".

    "Ob" as in "oblique" or "obtuse": Not a "right" as in not a right or acute angle, but an obtuse angle.

    Parallel: Never intersecting. Two lines are parallel if they will never intersect.

    Perimeter: The accumulative measurement of all sides of a polygon.

    Perpendicular: Intersecting at a right angle.

    Plane: The bases for most geometry terms. Can go on indefinitely and is named by at least three points that are not on the same line.

    Point: Used to define a certain area and represented by dots.

    Polygon: Is formed by sides with a common endpoint and which intersect two other sides at their endpoints.

    Postulate: A geometrical statement that is accepted as truth and describes a fundamental property.

    Prism: A solid with bases, lateral faces and lateral edges.

    Protractor: Tool used to measure degrees of an angle.

    Pyramid: All faces except the one base intersect at the same point and lateral faces that each form triangles.

    Radius: The line formed from the center of a circle to a point on the circle.

    Ratio: Comparing two numbers using division.

    Rectangle: A parallelogram with four right angles.

    Rhombus: A parallelogram with all four congruent sides.

    Right: Having 90 degree angle.

    Scalene: Having no two sides congruent.

    Secant: A line intersecting a circle in "exactly two points".

    Segment: Part of. As in a line segment is a part of the line itself.

    Slope: The measurement of a line having two points with two coordinates.

    Square: Quadrilateral with all four sides congruent.

    Tangent: Line in a plane intersecting a circle at only one point.

    Theorem: A statement that has yet to be proven true or untrue.

    Transversal: Intersects two lines in two different points.

    Trapezoid: Quadrilateral having only one pair of parallel sides.

    Triangle: Three sides whose endpoints are the endpoint of only one other side.

    Volume: The amount of enclosed space a figure creates.

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