INTRODUCTION TO PLANE GEOMETRY

1
UNIT 19

• INTRODUCTION TO PLANE GEOMETRY

2
GEOMETRY DEFINED

• Plane geometry deals with points, lines, and
  various figures that are made of combinations of
  points and line segments. The figures lie on a
  flat surface or plane
• In the study of plane geometry certain basic
  statements called axioms or postulates are
  accepted as true without requiring proof.
  Several of these axioms are stated below and on
  the following slide
• Quantities equal to the same quantities or to
  equal quantities are equal to each other

3
AXIOMS

• A quantity may be substituted for an equal
  quantity
• If equals are added to equals, the sums are equal
• If equals are subtracted from equals, the
  remainders are equal
• If equals are multiplied by equals, the products
  are equal
• If equals are divided by equals, the quotients
  are equal

4
AXIOMS

• The whole is equal to the sum of all its parts
• The whole is greater than any of its parts
• One and only one straight line can be drawn
  between two given points
• Through a given point, one and only one line can
  be drawn parallel to a given straight line
• Two straight lines can intersect at only one point

5
AXIOMS

• Identify the axiom that applies to each statement
  given below
• a. If ad ef, then 12ad 12ef
• Since equals are multiplied by equals, the axiom
  If equals are multiplied by equals, the products
  are equal applies here
• b. If x 2.5 and y 2.5, then x y
• The axiom Quantities equal to the same
  quantities or to equal quantities are equal to
  each other applies here

6
TERMS DEFINED

• A point is shown as a dot. It is usually named by
  a capital letter. A point has no size or form it
  has location only
• In this text, a line always means a straight
  line. A line extends without end in two
  directions. A line is usually named by two points
  on the line
• A curved line is a line, no part of which is
  straight
• A line segment is that part of a line that lies
  between two definite points. Line segments are
  often named by placing a bar over the end point
  letters

7
TERMS DEFINED

• Parallel lines do not meet regardless of how far
  they are extended. They are the same distance
  apart at all points
• The symbol means parallel
• Perpendicular lines meet or intersect at a right
  or 90 angle
• The symbol ? means perpendicular
• Oblique lines are neither parallel nor
  perpendicular. They meet or intersect at an angle
  other than 90?

8
PRACTICE PROBLEMS

• Identify the axiom that applies to the statements
  in problems 13
• 1. If a b, then a 9 b 9
• 2. Given x 2, y 3, and z x y, then z
  2 3 5
• 3. If a b and b c, then a c
• 4. Define a point
• 5. Define a line segment
• 6. Define perpendicular lines
• Write each statement in problems 7 and 8 using
  symbols
• 7. Segment CD is parallel to segment EF
• 8. Line AB is perpendicular to line GH

9
PROBLEM ANSWER KEY

• 1. If equals are subtracted from equals, the
  remainders are equal
• 2. A quantity may be substituted for an equal
  quantity
• 3. Quantities equal to the same quantities or
  to equal quantities are equal to each other
• 4. Shown as a dot. Has no size or form it has
  location only
• 5. The part of a line that lies between two
  definite points
• 6. Lines that meet or intersect at a right or
  90 angle
• 7. CD EF