INTRODUCTION TO PLANE GEOMETRY Unit 19 INTRODUCTION TO PLANE GEOMETRY

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.

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

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

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

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

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

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

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 = 2 + 3 = 5 If a = b and b = c, then a = c Define a point

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

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