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: plane j and plane k intersect at line \\( \overleftrightarrow { j k } \\)
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.
postulate 1.2e: if two planes intersect, they intersect in exactly one line.
postulate 1.2b. through any three noncollinear points there is exactly one plane.

1. choose the best answer.

identify the postulate illustrated by the statement: line \\( \overleftrightarrow { a b } \\) and line \\( \overleftrightarrow { c d } \\) intersect at point p.
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 1.2e: if two planes intersect, they intersect in 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.

Explanation:

For the first question, the statement is about two planes intersecting at a line. Postulate 1.2E specifically states that if two planes intersect, they intersect in exactly one line. For the second question, the statement is about two lines intersecting at a point. Postulate 1.2D states that if two lines intersect, they intersect at exactly one point.

Answer:

1. C. Postulate 1.2E: If two planes intersect, they intersect in exactly one line.
2. B. Postulate 1.2D: If two lines intersect, they intersect at exactly one point.