Download Section 10.1 – Points, Lines, Planes and Angles

Chapter 10. Section 1
Page 1
Section 10.1 – Points, Lines, Planes and Angles
Homework (pg 513) 1-2, 5-36
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Definition: A point is represented as a small dot and usually written as a capitol letter (point A). It
has no dimension, but merely specifies a place in space.
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Definition: A line connects two distinct points with the shortest possible distance (in other words it
is straight). It goes on forever in both directions. It is expressed with a lower case letter (line l) or
suur
suur
using the letters of each point next to each other with a line above (line AB or BA ).
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Definition: A plane is a flat surface with no boundaries, and it has no thickness. It is twodimensional, meaning you can move two different directions on that surface.
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Definition: We can take portions of lines. A line going in one direction is a ray. The ray has an
initial point (where it begins) and a terminal point (to specify where it heads). It is expressed with
uuur
suuu
the letters of the points (ray AB or BA , note the initial point has no arrow above it). A line
segment is just the portion of the line between two points known as endpoints. It is expressed
without arrowheads (line segment AB or BA ).
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Note that lines and line segments can be written with either point first, but for a ray you have to be
careful that the initial point has no arrowhead above it.
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Definition: An angle is formed by two rays that meet at their initial points, which is known as the
vertex of the angle. It has an initial side and a terminal side, which can be difficult to determine out
of context. Most angles are written in standard position on the two-dimensional x-y axis, which is
when the initial side is lined up with the positive x-axis and the vertex at the ordered pair (0,0)
Angles are named several ways. You can name the angle with three points (the vertex B and one
point on each ray, A&C) as R ABC or ∠ ABC or S ABC . Or you can just use the vertex as
R B or ∠ B or S B . Sometimes there is a greek letter inside the angle (between initial and
terminal sides) and you can use that letter R β or ∠ β or S β
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You measure angles by finding the amount of rotation from the initial side to the terminal side.
Angles can be measured in degrees (there are 360o in a circle) or radians (there are 2π radians in one
circle, π is approximately 3.14). Fractional components of degrees are minutes (60 minutes = 1
degree) or seconds (60 seconds = 1 minute). This is the same as time measurements… why?
Chapter 10. Section 1
Page 2
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There are special angles:
Right angle = 90 degrees
Straight angle = 180 degrees
Acute angle (between 0 and 90 degrees)
Obtuse angle (between 90 and 180 degrees)
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There are special relationships between angles:
Complementary (they sum to 90 degrees)
Supplementary (they sum to 180 degrees)
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Example: Find the angle measures in the diagram using the
definition of supplementary angles
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Notice any new special relationships in the diagram? Angles that are across a vertex from eachother
are called vertical angles, and their measures are the same
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When a parallel line is cut with another line, all the angles that correspond
have the same measure. These are called corresponding angles