Building Blocks Of Geometry

1. Building Blocks of Geometry

2. The Building Blocks
•Point
•Plane
•Line
•These 3 objects are used to make all of the
other objects that we will use in Geometry
•What do you think it means to be a “Building
block of Geometry? What might one be?

3. Point
•The most basic building block
•Has no size
•Only has a Location
•Representation
–Shown by a Dot
–Named with a single Capital letter
•Ex:
• What would a real world example be?
= “Point P”

4. Line
•A straight, arrangement of infinitely many
points.
•Infinite length, but no thickness
•Extends forever in 2 directions
•Named by any 2 points on the line with the
line symbol above the letters (order does not
matter
•Ex: = “Line AB” or “Line BA”
•Real World Example?

5. Plane
•An imaginary flat surface that is infinitely large and with zero
thickness
•Has length and width, but no thickness
•It is like a flat surface that extends infinitely along its length and
width
•Represented by a 4 sided figure, like a tilted piece of paper
–This is really only part of a plane
•Named with a Capital Cursive letter
•Ex:
P
= “Plane P”
•Real World Example?

6. Explaining the Objects
•Can be difficult
•Early Mathematicians attempted to:
•Ancient Greeks
•“A point is that which has no part. A line is a breathless
length.”
•Ancient Chinese Philosophers
•“The line is divided into parts, and that part which has
no remaining part is a point.”

7. What’s the Problem?

8. Definitions
•A definition is a statement that clarifies or
explains the meaning of a word or phrase
•It is impossible to define “point,” “line,” and “plane”
without using words or phrases that need to be
defined.
•Therefore we refer to these building blocks as “Undefined”
•Despite being undefined, these objects are the basis for all
geometry
•Using the terms “point,” “line,” and “plane,” we can
define all other geometry terms and geometric figures

9. Definitions
•Collinear – Lie on the same line
–Example – Points A and B are “Collinear”

10. Definitions
•Coplanar – Lie on the same plane
–Example – Point A, Point B, and Line CD are
“Coplanar.”

11. Definitions
•Line Segment – Two points (called endpoints)
and all of the points between them that are
collinear.
–In other words, a portion of a line
–Represent a Line Segment by writing its endpoints
with a bar over the top
–Example:

12. Definitions
•Ray – Begins at a single point and extends
infinitely in one direction
–Example:
–You need 2 points to name a ray, the first is the
endpoint, and the second is any other point that
the ray passes through.

13. Definitions
•Congruent – equal in size and shape
–We mark 2 congruent segments by placing the
same number of slash marks on them.
–The symbol for congruence is and you say it
as “is congruent to.”
–Example:

14. Definitions
•Bisect – Divide into 2 congruent parts
•Midpoint – the point on the segment that is
the same distance from both endpoints.
•The midpoint bisects the segment

15. Definitions
•Parallel Lines – 2 lines that never intersect
–We mark 2 lines as parallel by placing the same
number of arrow marks on them.
–Example:
–To write this as a statement, we would write

16. Definitions
•Perpendicular Lines – 2 lines that intersect at
a Right Angle (90°).
–We mark 2 lines as Perpendicular by placing a
small square in the corner where they cross
–Example:
–To write this as a statement, we would write:

17. •Things you may Assume
1)You may assume that lines are straight, and if 2
lines intersect, they intersect at 1 point.
2) You may assume that points on a line are
collinear and that all points & objects shown in a
diagram are coplanar unless planes are drawn to
show that they are not coplanar.

18. •Things you may NOT Assume
1)You may not assume that just because 2 lines,
segments, or rays look parallel that they are
parallel – they must be marked parallel
2)You may not assume that 2 lines are
perpendicular just because they look
perpendicular – they must be marked
perpendicular
3)Pairs of angles, segments, or polygons are not
necessarily congruent, unless they are marked
with information that tells you that they are
congruent.