Saved Bookmarks
| 1. |
Here are some of the fundamental postulates used in Geometry. 1. Two points determine exactly one line..2. Three noncollinear points are contained in at least one plane and three noncollinear points are con-tained in exactly one plan.3. If two distinct planes intersect, then their intersection is a line.4. If two points of a line are in plane, then the line is in the plane.5. There is one-to-one correspondence between the points of a line and the set of real numbers, such thatthe distance between any two points of the line is the absolute value of the difference between the cor-responding numbers.6. Given two points P and S on a line, a coordinate system van be chosen in such a way that the coordinateof Pis O and the coordinate of S is greater than 0.haber7. For every angle, there corresponds a unique real number r where 0 |
|
Answer» Postulate 1: A line contains at least two POINTS. Postulate 2: A plane contains at least three NONCOLLINEAR points. Postulate 3: Through any two points, there is exactly one line. Postulate 4: Through any three noncollinear points, there is exactly one plane. Postulate 5: If two points lie in a plane, then the line joining them lies in that plane. Postulate 6: If two planes intersect, then their INTERSECTION is a line. Theorem 1: If two lines intersect, then they intersect in exactly one point. Theorem 2: If a point lies outside a line, then exactly one plane contains both the line and the point. Theorem 3: If two lines intersect, then exactly one plane contains both lines. Example 1: State the postulate or theorem you would use to justify the statement made about each figure. Figure 1 Illustrations of Postulates 1–6 and Theorems 1–3. (a) Through any three noncollinear points, there is exactly one plane (Postulate 4). (b) Through any two points, there is exactly one line (Postulate 3). (c) If two points lie in a plane, then the line joining them lies in that plane (Postulate 5). (d) If two planes intersect, then their intersection is a line (Postulate 6). (e) A line contains at least two points (Postulate 1). (f) If two lines intersect, then exactly one plane contains both lines (Theorem 3). (g) If a point lies outside a line, then exactly one plane contains both the line and the point (Theorem 2). (h) If two lines intersect, then they intersect in exactly one point (Theorem 1).Step-by-step explanation: |
|