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