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 that
the 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 coordinate
of Pis O and the coordinate of S is greater than 0.
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7. For every angle, there corresponds a unique real number r where 0 <r< 180.
8. If Dis in the interior of angle ABC, then the measure of angle ABC is equal to the measure of angle ABD +
the measure of angle CBD.
9. If two angles from a linear pair, then they are supplementary.
Answers
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:
Answer:
Postulates:
Facts which are self evident and taken for granted in geometry are called Axioms.
Euclid's Postulates:
1. A straight line can be drawn from one point to another point.
2.terminated line segment can be extended indefinitely.
3.A circle can be drawn with any center and any radius.
4.All right angles are equal to one another.
5.If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles then the two straight lines, if produced indefinitely meet on that side on which the sum is less than two right angles.
6.Three non collinear points are contained in at least one plane and three non collinear points are contained in exactly one plan.
7.If two distinct planes intersect, then their intersection is a line.
8. If two points of a line are in plane, then the line is in the plane.
9. For every angle, there corresponds a unique real number r where 0 <r< 180.
10.If Dis in the interior of angle ABC, then the measure of angle ABC is equal to the measure of angle ABD +the measure of angle CBD.
11. If two angles from a linear pair, then they are supplementary.