Question

Ria plotted four points P, Q, R, and S on the chalkboard and joined segment PQ and segment RS using straight lines, as shown:

Answer 1

Ria made the following statements about the points.

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

Which chart best justifies Ria's statements?

Answer 2

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 3

Statement 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 4

Statement 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 5

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

Answer 6

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