POINTS, LINES, AND PLANES

1
POINTS, LINES, AND PLANES
2
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

3
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.

4

5

• Name a line containing point A.

• Name a plane containing point C.

6

• How many planes are shaded in the figure?

• Name three points that are collinear

• Are points A, C, D, and J Coplanar? Explain.

7
PRACTICE

• Pg. 9 13-17, 21-35

8
Linear Measure and Precision
9
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

10
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.
11
Examples
12
Practice

• Pg. 17 12-27, 34-39

13
Distance and Midpoints
14
Definitions

• Midpoint-the point halfway between two points
• Bisect-to cut in half

15
Midpoint Formula
Average the x's and average the y's
16
Examples

• Find the midpoint between (2,6) and (0,0)

• Find the midpoint between (-5,-3) and (7,9)

17
Distance Formula
18
Examples

• Find the distance between the points (2,5) and
  (5,9)

19
Examples

• Find the distance between the points (0,5) and
  (5,-7)

20
Practice

• Pg. 25 13-22

21
ANGLE MEASURE
22
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.

23
DEFINITIONS

• Interior inside of the angle.

• Exterior outside of the angle.

24
ANGLE CLASSIFICATIONS

• Right angle 1/4 of a circle 90 degrees

• Obtuse greater than 90 degrees

• Acute less than 90 degrees

25
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

26
EXAMPLES
Angle RQT47
27
EXAMPLES
Angle TQS22
28
PRACTICE

• Pg. 34 12-23

29
ANGLE RELATIONSHIPS
30
DEFINITIONS

• Adjacent Angles Angles that share a side and do
  not overlap

• Vertical Angles two nonadjacent angles formed by
  two intersecting lines

31
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.

32
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
33
EXAMPLES
34
PRACTICE

• Pg 42 11-35

35
POLYGONS
36
DEFINITIONS

• Polygon a closed figure where all sides are
  segments

• Not Polygons

• Polygons

• Regular Polygon a polygon where all sides and
  all angles are congruent

37
DEFINITIONS

• Concave and Convex

• Concave

• Convex

• Trick to remember Concave figures have "hiding
  spots," just like a cave.

• Perimeter the sum of the lengths of the sides of
  a polygon.

38
NAMES OF POLYGONS
39
EXAMPLE
40
EXAMPLE
41
EXAMPLE
WORK THROUGH ON BOARD
16 UNITS
42
PRACTICE

• Pg. 48 12-31

43
(No Transcript)