Question

determine if each of the following statements are true or false. if false, explain why. a. two intersecting lines are coplanar. b. three noncollinear points are always coplanar. c. two planes can intersect in exactly one point. d. a line segment contains an infinite number of points. e. the union of two rays is always a line. b. the statement is false because they can only intersect in a line. c. the statement is false because they intersect in exactly two points. d. the statement is true. d. choose the correct answer below. a. the statement is true. b. the statement is false because a line segment only contains the points between the defined endpoints. c. the statement is false because the number of points a line segment contains depends on its length. d. the statement is false because a line segment only contains the two endpoints. e. choose the correct answer below. a. the statement is false because the union of two rays is always a line segment. b. the statement is false because the union of two rays is always a plane. c. the statement is true. d. the statement is false because the union of two rays can be a single ray.

Explanation:

Step1: Analyze statement a

Two intersecting lines lie in the same plane, so it's true.

Step2: Analyze statement b

Three non - collinear points determine a plane, so it's true.

Step3: Analyze statement c

Two planes intersect in a line, not a point, so it's false.

Step4: Analyze statement d

A line segment has an infinite number of points between its endpoints, so it's true.

Step5: Analyze statement e

The union of two rays can be a single ray, not always a line, so it's false.

Answer:

a. True
b. True
c. B. The statement is false because they can only intersect in a line.
d. A. The statement is true.
e. D. The statement is false because the union of two rays can be a single ray.