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 • Collinear: on the same line • Coplanar: in the same plane • Space: a boundless three-dimensional set of all points • Locus: a set of points that satisfies a particular condition.

• 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 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 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 • C • Name the sides of angle 4 • BA and BC • What is another name for angle BDC • 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.

Name a pair of adjacent angles One example: VZX AND XZW Name a pair of vertical angles EXAMPLES 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: • 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