Question

Ria plotted four points P, Q, R, and S on the chalkboard and joined and using straight lines, as shown.



Ria made the following statements about the points.

Statement 1: Point P and Point Q are contained on one line.
Statement 2: and intersect at only one point.

Which chart best justifies Ria’s statements?

Answer 1

a) Statement
Justification
1
Postulate: If two distinct points are given, then a unique line contains them.
2
Postulate: If two lines intersect, then they intersect in exactly one point.

Answer 2

b) Justification
1
Postulate: If a point lies outside a line, then exactly one plane contains both the line and the point.
2
Theorem: If two lines intersect, then they intersect in exactly one point.

Answer 3

c) Justification
1
Theorem: Through any two points there is exactly one line.
2
Theorem: If two distinct planes intersect, then they intersect in exactly one line.

Answer 4

d) Justification
1
Postulate: If two distinct points are given, then a unique line contains them.
2
Theorem: Through any three non collinear points, there is exactly one plane.

Answer 5

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