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Chapter 1
Foundations for Geometry
Students’ Presentation
1-1 Points, Lines, and Planes
By…
Definition
•
Points: Points are the simplest figures in geometry. A point has no
size, although it may represent an object with size. It is shown
pictorially as a dot and is usually named using a capital letter. All
geometric figures consist of points.
•
Line: A line is a set of points that originate from one point and extend
indefinitely in two opposing directions. Often, a line is named by a
lower case letter; if a line contains two points A and B, then the line
can be denoted as AB or BA. Lines have no thickness, even though
pictorial representations of lines do.
•
Plane: A plane can be modeled by a floor, a table top or a wall. Planes
extend indefinitely in all directions and have no edges or thickness.
Planes are often denoted by a single capital letter and represented as
four-sided figures.
Characteristics
• Point- you find them easily on lines and on
coordinate planes.
• Line- they are everywhere. But in
geometry you find them in angles,
coordinate planes, and just as themselves.
• Planes- they are very obviously found, they
are shapes.
Examples in real life
1-2 Segments
By
Definition
-A segment of a line consisting of two endpoints and all
points between them
-In other words, A line that contains two end points,
which may contain points in the middle
Characteristics
• Two End points
• Length can be defined(unlike a line)
Examples in real life
1-3 Angles
Definition
•The amount of turn between
two straight lines that have a
common end point which is the
vertex.
Characteristics






Acute angle less than 90
Right angle exactly 90
Obtuse angle between 90 and 180
straight angle exactly 180
Reflex angle between 180 and 360
Full angle exactly 360
Characteristics
. Acute angle-An angle less than 90°
. Obtuse angle-An obtuse angle is one which is
more than 90° but less than 180°
.Right angleAn angle which is equal to 90°, one quarter of a full
revolution
Examples in real life:
1-4 Pairs of Angles
By
Definition
-congruent angles: angles that have the same measure
-vertical lines: are the opposite angles formed by two
intersecting lines
-adjacent lines: pair of angles that share a vertex and one side
but do not overlap, no congruent sides
-linear lines: a straight line divided by a ray, not congruent
lines
-complementary angles: two angles whose measures have a sum
of 90 degrees
-supplementary angles: two angles whose measures have a sum
of 180degrees
Characteristics
• Vertical angles – Are always congruent
• Linear pairs – Add to 180 degrees, also
adjacent
• Adjacent Angles – Have common side,
don’t overlap, common vertex
• Complementary Angles – Are 90 degrees
• Supplementary Angles – Are 180 degrees
Examples in real life
Supplementary Angles
Adjacent Angles
Vertical Angles
Angles 1 and 2 are Linear Pair
Complementary Angles
1-6 Midpoint and
Distance
By
Definition
Mid-point -The exact middle point
“the midpoint of the line segment”
Distance- The distance between two
points of a straight line that links
them.
Definition
 Midpoint of a line segment is the point
that is halfway between the endpoints of
the line segment
 Distance is an amount of space between
two things
Characteristics
Midpoint:
 Middle or center
 Midpoint Equation:
Distance:
 Always positive
 Length
 Distance Equation:
Examples in real life
Examples in real life
1-7 Transformations
Definition
1. "Rotation" means turning
around a center.
2.A reflection is a flip over a
line.
3."Translation" simply means
moving, without rotating,
resizing or anything else, just
moving.
EXAMPLES IN REAL LIFE
THERE ARE 41 JOBS THAT USE TRANSFORMATIONS.
HERE ARE A FEW:
CONSTRUCTION AND BUILDING INSPECTORS
DESKTOP PUBLISHERS
GLAZIERS
ACTUARIES
MATHEMATICIANS
STATISTICIANS
MACHINISTS
CHAPTER 1
Class Activity
Find measures of all angles. Then classify the angles as acute,
right, or obtuse.