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Chapter 1: Q18. (page 30)

Classify each statement as true or false.

It is possible for two intersecting lines to be non-coplanar.

Short Answer

Expert verified

The given statement that It is possible for two intersecting lines to be non-coplanar is False.

Step by step solution

01

Step 1. Write the Theorem 1-3.

The Theorem 1-3 states that if there are two intersecting lines, then exactly one plane can pass through these lines.

02

Step 2. Draw two intersecting lines and plane containing these lines.

03

Step 3. State whether the given statement is true or false by considering the Theorem 1-3 and the diagram.

From the diagram and Theorem 1-3 it can be concluded that:

If there are two lines which are intersecting then exactly one plane can pass through these lines.

Therefore, if the two lines are intersecting then surely one plane will pass through these line therefore, the two intersecting lines will never be non-coplanar.

Hence the given statement that It is possible for two intersecting lines to be non-coplanar is false.

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Most popular questions from this chapter

From the following figure, name the ray opposite to SP鈫�.

Name a point on STthat is not on ST.

Points R,S andT are non collinear points.

  1. State the postulate that guarantees the existence of a plane X that contains R,S and T.
  2. Draw a diagram showing planeX containing the non collinear points R,S and T.
  3. Suppose thatP is any point ofRS鈫� other thanR and S. Does pointP lie in plane X? Explain.
  4. State the postulate that guarantees thatTP鈫� exists.
  5. State the postulate that guarantees thatTP鈫� is in plane X.

For the following symbols, find the symbols that represent a line, segment, ray, or length.

a. PQ炉

b. PQ鈫�

c. PQ鈫�

d. PQ

Classify each statement as true or false.

A, B, C, and D are coplanar.
See all solutions

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