Q20. - Geometry

Question

Classify each statement as true or false.

If points $A$ and $B$ lie in plane $P$, then so does any point of $\overleftrightarrow{AB}$.

Step-by-Step Solution

Answer

The given statement that if points $A$ and $B$ lie in plane $P$, then so does any point of $\overleftrightarrow{AB}$ is True.

Step 1. Write the postulate 8.

The Postulate 8 states that if there are two points in a plane then the line joining these points also lies on that plane.

Step 2. Draw a plane containing the two points and the line joining these two points.

Step 3. State whether the given statement is true or false by considering the postulate 8 and the diagram.

From the diagram and postulate 8 it can be concluded that:

If two points lie on the plane then the line joining these points also lies on the plane.

Therefore, if there are two points $A$ and $B$ lying on the plane $P$, then the line joining these two points that is the line $\overleftrightarrow{AB}$ will also lie on the plane $P$.

Therefore, consequently any point of $\overleftrightarrow{AB}$ will lie on the plane $P$.

Hence the given statement that that if points $A$ and $B$ lie in plane $P$, then so does any point of $\overleftrightarrow{AB}$ is true.