Q18.
Question
Classify each statement as true or false.
It is possible for two intersecting lines to be non-coplanar.
Step-by-Step Solution
Verified Answer
The given statement that It is possible for two intersecting lines to be non-coplanar is False.
1Step 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.
2Step 2. Draw two intersecting lines and plane containing these lines.
3Step 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.
Other exercises in this chapter
Q16.
DB→ bisects ∠ADC, m∠1=5x−3, and m∠2=x+25. Find the value of x.
View solution Q17.
Classify each statement as true or false.It is possible to locate three points in such a position that an unlimited number of planes contain all three points.
View solution Q19.
Classify each statement as true or false.Through any three points there is at least one line.
View solution Q20.
Classify each statement as true or false.If points A and B lie in plane P, then so does any point of AB↔.
View solution