Definitions of Geometric Terms

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Presentation transcript:

Definitions of Geometric Terms

undefined term POINT: described as the basic unit of geometry; it is infinitely small, it has only location and no size; grain of sand or ballpen tip illustrates a point. Examples: Point A or Point B. . A B

Name a line by determining 2 points on the line: undefined term LINE: described as a straight continuous arrangement of an infinite number of points; has infinite length but no thickness; extends in two opposite directions; Name a line by determining 2 points on the line: A B

undefined term PLANE: described as having length and width but no thickness; like a flat surface that extends forever along its length and width; represented by a four-sided figure. A B . X Y

Definitions COLLINEAR: Being on the same line / Collinear points are points that lie on the same line. COPLANAR: Being on the same plane / Coplanar points/lines are points/lines that lie on the same plane.

Definitions Is it necessary to say “two collinear points”? No. Two points already determine a line. A line exists connecting any two distinct points. Can a point and a line be coplanar? Yes.

Definitions SPACE: Defined as the set of all points. A B . X Y

Take note! Two distinct points determine a line. Three distinct collinear points determine at least 1 plane. Three distinct non-collinear points determine a unique plane. How many planes are determined by 4 non-collinear points? How many planes are determined by 5 points, three of which are collinear?

Imagine or illustrate... A line intersecting a point Two intersecting lines A line contained in a plane A plane intersecting a line at exactly one point Two distinct planes that do not intersect Two intersecting (but not overlapping) planes

Definitions How do we define “BETWEEN”? F A B C D E G H B is between A and C. C is between A and D. “between-ness” assumes that the points are collinear. F is NOT between B and E. H is NOT between D and E.

Definitions LINE SEGMENT: Defined as part of a line; consists of two points (endpoints) and all points between them Segment AB (point A and point B as endpoints) A B Segment AB

Definitions How do we measure segments? A B C D E 3 2 12 the measure of a segment is usually written on the middle portion of the segment.

Definitions How do we measure segments? A B C D E 3 2 12 What is AC? BD? BE? AE?

Take note! SEGMENT ADDITION POSTULATE A B C If A, B, and C are collinear such that B is between A and C, then AB + BC = AC.

Definitions Congruent figures! Equal measures! CONGRUENT SEGMENTS: Two segments are congruent segments if and only if they have the same length. Congruent figures! Equal measures! If segment AB is CONGRUENT with segment CD, then the measure of length of segment AB is EQUAL to the measure of length segment CD.

Definitions MIDPOINT OF A SEGMENT: If X is the midpoint of , then X is a point on such that AX=XB. A X B The midpoint of a segment divides the segment into 2 congruent parts. It becomes a segment bisector.

Try this! Given: Segment A, where AX is equal to XB. A B X Therefore, AX is congruent to XB. Is Point X a midpoint of Segment AB? Always, Sometimes, Never? Sometimes. Point X is a midpoint if it lies on segment AB.