1. INTRODUCTION TO PLANE GEOMETRY
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.

3. AXIOMS
Quantities equal to the same quantities or to equal quantities are equal to each other
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:
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
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.
Extends without end in two directions.
Is usually named by two points on the line

7. TERMS DEFINED (Cont) A curved line is a line,
No part of a curved line 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

8. TERMS DEFINED (Cont) The symbol || means parallel
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

9. PRACTICE PROBLEMS
Identify the axiom that applies to the statements in problems 1–3:
If a = b, then a – 9 = b – 9
Given: x = 2, y = 3, and z = x + y, then z = = 5
If a = b and b = c, then a = c
Define a point

10. PRACTICE PROBLEMS (Cont)
Define a line segment
Define perpendicular lines
Write each statement in problems 7 and 8 using symbols:
Segment CD is parallel to segment EF
Line AB is perpendicular to line GH

11. PROBLEM ANSWER KEY
If equals are subtracted from equals, the remainders are equal
A quantity may be substituted for an equal quantity
Quantities equal to the same quantities or to equal quantities are equal to each other
Shown as a dot. Has no size or form; it has location only
The part of a line that lies between two definite points
Lines that meet or intersect at a right or 90° angle
CD || EF