Foundations for Geometry Chapter 1
By: Peter Spencer
Maria Viscomi
Ian McGreal
1.1 Understanding Points, Lines, and
Planes
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Undefined Term-can not be defined by using figures
Point- names a location and has no size, it is
represented by a dot; named with a capital letter
Line- is a straight path that has no thickness and
extends forever; named with a lowercase letter or
two points on the line
Plane-a flat surface that has no thickness and
extends forever; named by a script capital letter or
three points not on a line
Collinear- points on the same line
Coplanar- points on the same plane
1.1 Continued
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Segment (or line segment)- the part of a line consisting of two
points and all the points between them; named by its two
endpoints
Endpoint- point at the end of a segment or the starting point of
a ray; named by a capital letter
Ray- part of a line that starts at an endpoint and extends
forever in one direction; named by
its endpoint and any
other point on the ray
Opposite Rays- two rays that have a common endpoint and
form a line; named by common endpoint and any other point on
each ray
Postulate- a statement that is accepted as true without proof
1.2 Measuring and Constructing
Segments
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Coordinate- a number used to identify the location of a point
Distance- absolute value of the difference of the coordinates
Length- distance between two points
Congruent Segments- segments that have the same length
Construction- way of creating a figure that is more precise
Between- a point in between two points is between them
Midpoint- point that bisects
Bisects- divides a segment into two congruent segments
Segment bisector- any ray, segment, or line that intersects a
line at the midpoint
1.3 Measuring and Constructing
Angles
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Angle- figure formed by two rays, or sides,
with a common endpoint
Vertex- the common endpoint in an angle
Interior of an angle-the set of all points
between the sides of an angle
Exterior of an angle- the set of all points
outside the angle
Degree- 1/360th of a circle; what angles are
measured in
1.3 Measuring and Constructing
Angles
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Acute Angle- an angle measured greater than 0 but
less than 90
Obtuse Angle- an angle measured greater than 90
but less than 180
Right Angle- an angle measured 90
Straight Angle- an angle measured 180
Congruent Angles- angles with the same measure
Angle Bisector-a ray that divides and angle into two
congruent angles
1.4 Pairs of Angles
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Adjacent angles- two angles in the same plane with
a common vertex and a common side, but no
common interior points
Linear pair- pair of adjacent angles whose noncommon sides are opposite rays
Complementary angles- two angles whose
measures have a sum of 90
Supplementary angles- two angles whose measures
have a sum of 180
Vertical angles- two nonadjacent angles formed by
two intersecting lines
1.5 Using Formulas in Geometry
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Perimeter- sum of the side lengths of the figure
Area- number of non-overlapping square units of a given size
that exactly cover the figure
Base- any side of a triangle
Height- segment from a vertex that forms a right angle with a
line containing the base
Diameter- a segment that passes through the center of a circle
and whose endpoints are on the circle
Radius- a segment whose endpoints are the center of the circle
and a point on the circle
Circumference- distance around a circle
Pi- an irrational number; 3.14159265…..
1.6 Midpoint and Distance in the
Coordinate Plane
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Coordinate plane- a plane that is divided into four
regions by a horizontal and a vertical line
Leg- two sides that form the right angle of a right
triangle
Hypotenuse- the side across from the right angle
that stretches from one leg to the other
1.7 Transformations In the Coordinate
Plane
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Transformation- change in the position, size, or
shape of a figure
Preimage- the original figure before transformation
Image- the figure after transformation
Reflection- (flip) a transformation across a line
Rotation- (turn) transformation about a point
Translation- (slide) transformation in which all points
move the same distance and direction