TTO S MATHEMATICS 7 / CHAPTER 3 / MEASUREMENT EDU 1972 CHAPTER 7 GEOMETRY 7.1 INTRODUCTION OF GEOMETRY Geometry comes from the greek word "geometria", where in "geo" means earth then "metria" means measuring. Geometry is the study of properties and relationships of points, lines, angles, curves, surfaces and solids. GEOMETRIC RULES a. Postulate - It is a fundamental fact. It is a statement that seems to be obvious and is therefore accepted without a proof. b. Theorem - It is a rule that has been proven to be true from postulates and other theorems. c. Corollary - It is a statement that follows from the proof of another and does not require separate proof. d. Conjecture - It is the conclusions based on the observation. BASIC CONCEPTS AND TERMS (Undefined Terms) 1. POINT is an idea. It has no dimension at all but It can be represented by a dot, and it is denoted by a capital letter. · A · B ·M ·T 2. LINE is an infinite set of point extending infinitely (without end) in opposite directions. A line is one dimensional, that is it has length only. A line is named by two distinct points on it or by a lower case letter. A B m
O SR ATION MATHEMATICS 7 / CHAPTER 3 / MEASUREMENT EDUA 3. PLANE is two dimensional, that is, it has length and width but it has no height. It extends infinitely in all four directions. It is represented by a four sided figure. It is names using three points not in the same line or by a greek alphabet. SCHOOL LOS KHE 1972 ·A . C B Plane ABC OTHER TERMS 4. SPACE is a collection of all points. 5. COLLINEAR means to lie on the same line. 6. COPLANAR means to lie on the same plane. Postulates · Two points determine a line. · Three non-collinear points determine a plane. Exercises A. Determine if each of the following suggests a point, a line or a plane. 1. Sugar 2. Edge of a table 3. Corner of a room 4. Tip of a pen 5. Curtain rod 6. ceiling 7. floor 8. stars in the sky 9. fold on a paper 10. electrical wires B. Illustrate each of the following and label the diagram. 1. Point B lies in plane M. 2. Lines l and m intersect at point E. 3. Plane A contains line CD 4. Plane A and plane B intersect at line PR. 5. Point R is between the line MC. C. Describe each set of points as collinear or non-collinear. 1. {V,E,L} 2. {M,W,S} 3. {D,I,M,S} 4. {O,W,M,I} 5. {L,O,V,E} W L H O V E D S M I
TTO S MATHEMATICS 7 / CHAPTER 3 / MEASUREMENT EDUA LATION HIGH S SCHOOL 1972