WARM UP What do you think the following items have to do with Geometry? Write down your ideas on a sheet of paper. Discuss with your table groups. Assign one person in your group to share out your ideas. P Line Plane

BUILDING BLOCKS OF GEOMETRY

OBJECTIVES Learn the technology and notation of points, segments, lines, rays, planes, angles and collinear and coplanar. Learn the idea of congruence of line segments. Learn how to mark congruence of segments on diagrams Begin keeping a notebook of definition. Practice cooperative behavior.

INTRODUCTION A mathematical definition of a term gives its meaning using only previously defined mathematical terms and common words like “the” and “any” Try to arrange the terms point, line, line segment, midpoint and plane in an appropriate order and write mathematical definitions for them.

DEFINITIONS It can be difficult to explain what points lines and planes are even though you may recognize them. Early mathematicians tried to define them.

DEFINITIONS The Greeks said, “A point is that which has no part. A line is breadthless length.” Chinese philosophers said, “The line is divided into parts, and that part which has no remaining part is a point.” A definition is a statement that clarifies or explains the meaning of a word of phrase. It is impossible to define point, line, and plane without using words or phrases that themselves need definition. So the three terms, POINT, LINE and PLANE remain undefined but are the BASIS for all of geometry. Using these terms you can define all other geometry terms and figures.

TRY THIS… Ball A is in the pocket of the man. Ball C is on the woman’s racquet. All other balls are on the tennis court. 1.Name three balls that are collinear. 2.Name three balls that are coplanar but not collinear 3.Name four balls that are not coplanar.

DEFINITIONS A line segment consists of two points called endpoints of the segment and all the points between them that are collinear with two points. Draw what you think that might look like. Compare your drawings in your table groups and discuss which ones are correct. You can write line segment AB, using a segment symbol, as AB or BA. There are two ways to write the length of a segment.

DEFINITIONS Two segments are congruent, if and only if they have equal measures, or lengths. The symbol ≅ means congruent.

DEFINITIONS When drawing figures, you show congruent segments by making identical marks, called “tick marks.”

DEFINITIONS The midpoint of a segment is the point on the segment that is the same distance from both endpoints. The midpoint bisects the segment, or divided the segment into two congruent segments. Study the diagram below: –Name each midpoint and the segment it bisects –Name all the congruent segments. Use the congruence symbol to write your answers.

DEFINITIONS A ray begins at a point and extends infinitely in one direction. Draw what you think that would look like. Share your drawing with your group and decide which ones are correct.

CH. 1.1 INVESTIGATION In this lesson, you encountered many new geometry terms. In this investigation work in your groups to identify models from the real world that represent these terms and to identify how they are represented in in diagrams. Complete the investigation and submit your answers via DP.net

CH. 1.1 CONCEPTS PRACTICE Complete Steps 1 through 4.