POINTS, LINES, AND PLANES

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Transcript POINTS, LINES, AND PLANES

POINTS, LINES, AND
PLANES
UNDEFINED TERMS
•
Terms defined only by examples and descriptions
•
Point: a location
•
Line: a set of points that goes on infinitely in both
directions and has no thickness or width
•
Plane: a flat surface made up of points
OTHER VOCABULARY
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Collinear: on the same line
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Coplanar: in the same plane
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Space: a boundless three-dimensional set of all points
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Locus: a set of points that satisfies a particular
condition.
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Name a line containing
point A.
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Name a plane containing point
C.
•
How many planes are shaded in the
figure?
• Name three points that are collinear
• Are points A, C, D, and J Coplanar?
Explain.
PRACTICE
Pg. 9 #13-17, 21-35
Linear Measure and
Precision
Definitions
• Line Segment: The part of a line between two
end points
• Precision: a measurement precise to within .5
units of measure
• Between: point M is between points P and Q
only if PM + MQ = PQ
• Congruent: exactly the same size and shape
Examples
Find the precision for each measurement:
A. 5 millimeters
Since the measurement is accurate to the nearest
millimeter, the measurement must be accurate to the
nearest .5 millimeter. So the precision is from 4.5 to 5.5
millimeters.
B. 8 1/2 inches
Since the measurement is accurate to the nearest 1/2
inch, the measurement must be accurate to the nearest
1/4 inch. So the precision is from 8 1/4 inches to 8 3/4
inches.
Examples
Practice
Pg. 17 #12-27, 34-39
Distance and
Midpoints
Definitions
Midpoint-the point halfway between two points
Bisect-to cut in half
Midpoint Formula
Average the x's and average the y's
Examples
•
Find the midpoint between (2,6) and (0,0)
• Find the midpoint between (-5,-3) and (7,9)
Distance Formula
Examples
•
Find the distance between the points (2,5) and
(5,9)
Examples
• Find the distance between the points (0,5) and
(5,-7)
Practice
Pg. 25 #13-22
ANGLE MEASURE
DEFINITIONS
•
Ray: a part of a line from one endpoint extending
infinitely in one direction.
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Angle: two rays that share an endpoint.
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Vertex: the common endpoint of the two rays in an
angle.
DEFINITIONS
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Interior: inside of the angle.
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Exterior: outside of the angle.
ANGLE CLASSIFICATIONS
•
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Right angle: 1/4 of a circle; 90 degrees
Acute : less than 90
degrees
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Obtuse : greater than 90
degrees
EXAMPLES
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Name the vertex of angle
2
•C
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Name the sides of angle
4
•
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BA and BC
What is another name for angle
BDC
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Angle CDB or Angle
1
EXAMPLES
Angle RQT=47
EXAMPLES
Angle TQS=22
PRACTICE
Pg. 34 #12-23
ANGLE RELATIONSHIPS
DEFINITIONS
• Adjacent Angles: Angles that share a side and do not
overlap:
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Vertical Angles: two nonadjacent angles formed by two
intersecting lines:
•
DEFINITIONS
Linear pair: a pair of adjacent angles that form a
straight line:
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Complementary Angles: a pair of angles whose sum is
90 degrees
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Supplementary Angles: a pair of angles whose sum is
180 degrees
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Perpendicular: lines that form right angles.
EXAMPLES
Name a pair of
adjacent angles
One example:
VZX AND XZW
Name a pair of
vertical angles
VZX and YZW or
VZY and XZW
Name a linear
pair
Two examples:
VZX and YZW or
VZY and WZW
EXAMPLES
PRACTICE
•
Pg 42 #11-35
POLYGONS
DEFINITIONS
•
Polygon: a closed figure where all sides are segments
• Polygon
• Not
s:
Polygons:
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Regular Polygon: a polygon where all sides and all
angles are congruent
DEFINITIONS
•
•
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Concave and Convex:
• Convex:
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Concave:
Trick to remember: Concave figures have "hiding
spots," just like a cave.
Perimeter: the sum of the lengths of the sides of a
polygon.
NAMES OF POLYGONS
EXAMPLE
EXAMPLE
EXAMPLE
WORK THROUGH ON BOARD
16 UNITS
PRACTICE
Pg. 48 #12-31