Question

unit 1 quiz 1
geometry a / unit 1 - the basics of geometry

1. choose the best answer.

identify the postulate illustrated by the statement: point f and point g lie on plane r, so line \\( \overleftrightarrow { f g } \\) lies on plane r.
postulate 1.2b: through any three noncollinear points there is exactly one plane.
postulate 1.2d: if two lines intersect, they intersect at exactly one point.
postulate 1.2a: through any two points there is exactly one line.
postulate 1.2c: if two points lie on a plane, then the line that contains those two points also lies on the plane.

1. choose the best answer.

identify the postulate illustrated by the statement: if the line \\( \overleftrightarrow { l m } \\) intersects line \\( \overleftrightarrow { m o } \\), points l, m, and o are all on the same plane.
postulate 1.2b: through any three noncollinear points there is exactly one plane.
postulate 1.2d: if two lines intersect, they intersect at exactly one point.
postulate 1.2c: if two points lie on a plane, then the line that contains those two points also lies on the plane.
postulate 1.2a: through any two points there is exactly one line.

Explanation:

For the first question, the statement is about two points on a plane and the line containing them also being on the plane. Postulate 1.2C directly addresses this situation.
For the second question, when two lines (which are sets of points) intersect, the three - point (two from one line, one common intersection point) situation (assuming non - collinear in a non - degenerate case) is covered by Postulate 1.2B which is about three non - collinear points and a plane.

Answer:

1. Postulate 1.2C: If two points lie on a plane, then the line that contains those two points also lies on the plane.
2. Postulate 1.2B: Through any three noncollinear points there is exactly one plane.