Math Problem Solver

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Part 1

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.

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Part 1

a. Choose the correct answer below.

A.

The statement is false because the two lines could be coplanar or they could be noncoplanar.

B.

The statement is true.

C.

The statement is false because the two lines could be skew lines and would be noncoplanar.

D.

The statement is false because the two lines could be parallel.

Part 2

b. Choose the correct answer below.

A.

The statement is false because the three points are noncollinear which means they do not lie on a single line.

B.

The statement is false because three noncollinear points are always noncoplanar.

C.

The statement is false because the three points can be coplanar but they could also be noncoplanar.

D.

The statement is true.

Part 3

c. Choose the correct answer below.

A.

The statement is false because they can intersect in a​ line, the empty​ set, or a plane.

B.

The statement is true.

C.

The statement is false because they intersect in exactly two points.

D.

The statement is false because they can only intersect in a line.

Part 4

d. Choose the correct answer below.

A.

The statement is false because the number of points a line segment contains depends on its length.

B.

The statement is false because a line segment only contains the points between the defined endpoints.

C.

The statement is false because a line segment only contains the two endpoints.

D.

The statement is true.

Part 5

e. Choose the correct answer below.