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.

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Presentation transcript:

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

Examples Find 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

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. 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.

EXAMPLES Name a pair of adjacent angles Name a pair of vertical angles Name a linear pair One example: VZX AND XZW VZX and YZW or VZY 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 Polygon s: 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

WORK THROUGH ON BOARD 16 UNITS

PRACTICE Pg. 48 #12-31