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POINTS, LINES, AND PLANES
UNDEFINED TERMS
•Point: a location
•Terms defined only by examples and descriptions
•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•Collinear: on the same line
•Space: a boundless three-dimensional set of all points
•Locus: a set of points that satisfies a particular condition.
•Coplanar: in the same plane
•Name a line containing point A.
•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
ExamplesFind the precision for each measurement:
A. 5 millimeters
B. 8 1/2 inches
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.
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
DefinitionsMidpoint-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.
•Angle: two rays that share an endpoint.
•Vertex: the common endpoint of the two rays in an angle.
DEFINITIONS•Interior: inside of the angle.
•Exterior: outside of the angle.
ANGLE CLASSIFICATIONS•Right angle: 1/4 of a circle; 90 degrees
•Acute : less than 90 degrees
•Obtuse : greater than 90 degrees
EXAMPLES•Name the vertex of angle 2
•Name the sides of angle 4
•What is another name for angle BDC
•C
•BA and BC
•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:
•Vertical Angles: two nonadjacent angles formed by two intersecting lines:
DEFINITIONS•Linear pair: a pair of adjacent angles that form a straight line:
•Complementary Angles: a pair of angles whose sum is 90 degrees
•Supplementary Angles: a pair of angles whose sum is 180 degrees
•Perpendicular: lines that form right angles.
EXAMPLESName a pair of adjacent angles
Name a pair of vertical angles
Name a linear pair
One example: VZX AND XZW
VZX and YZW orVZY and XZW
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
•Polygons:
•Not Polygons:
•Regular Polygon: a polygon where all sides and all angles are congruent
DEFINITIONS•Concave and Convex:•Convex
:•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