The Building Blocks of Geometry Points Line Plane

The Building Blocks of Geometry • Points • Line • Plane Q: These terms are called undefined terms. Why? 1

In geometry, definitions are formed using known words or terms to describe a new word. A formal definition states what the term being defined is and how it differs from others like it. There are three words in geometry that are not formally defined, but there is an agreement about what they mean. These three undefined terms are point, line and plane. 2

Points Point - a location in space. It has no size. It is named by a capital letter. . A Points are usually represented with a capital letter, but in the coordinate plane a point is represented as an ordered pair (x, y).

Points Can anyone identify examples of points in the real world? 4

Lines line - a series of points that extends in two opposing directions without end. Lines have no thickness. Q S Lines can be represented by two points on the line. Example: QS or SQ On the coordinate plane a line could be represented as an equation relating a set of points.

Lines Write the equation of a line through the points D(2, 9) and C(3, 24). Also, represent it symbolically (not graphically). 6

Line Segments Line segment - a part of a line with two endpoints. B R A segment is named by its endpoints. Example: RB or BR

Line Segments Why is a line segment a defined term if a line is considered undefined? 8

Rays Ray - consists of an endpoint and all the points of a line on one side of the endpoint. C D Read it as: “Ray CD” (the order does matter) Write it as: CD

True or false, ray NQ has another name. If true, what is the name? Name a pair of opposite rays. 10

Planes plane - a flat surface with no thickness that extends without end in all directions. http: //www. mathsisfun. com/geometry/plane. html What is wrong geometrically with the. gif in the link above? 11

Identify which of the following apply. When two planes intersect, ____ line(s) are formed. 0 1 2 3 Infinity 12

True or False: If two lines do not intersect, then they are parallel. If two lines are parallel, then they do not intersect. If two lines intersect, then they are not parallel. Hint: Look for counterexamples (they fit the first part of the statement but not the second). 13

Planes Intersecting lines - cross (intersect) at exactly one point. Parallel lines – do not intersect, but on the same plane. Skew lines – do not intersect, but are on a different plane.

• Collinear Points • Coplanar points • Opposite rays 15

• Collinear Points - points that lie on the same line. • Coplanar points - points that lie in the same plane. • Opposite rays - 2 rays that lie on the same line, with a common endpoint and no other points in common. Opposite rays form a straight line and/or a straight angle (180°: ). 16

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Congruent Segments Two segments are congruent if and only if they have equal lengths. You can show two segments are congruent by making identical markings. 19

Group Investigation With your partner… Look around the classroom and identify examples of each of these terms: point, line, plane, line segment, congruent segments, midpoint of a segment, parallel line segments and ray. 20