Q10. - Geometry

Question

Apply postulates and theorems to complete the statements.

If points $\mathbf{A}$ and $\mathbf{B}$ are in-plane $\mathbf{Z}$, $\underset{\mathbf{¯}}{\mathbf{?}}$.

Step-by-Step Solution

Answer

The complete statement is:

If points $A$ and $B$ are in plane $Z$, then the line $\mathbf{AB}$ will also lie on the plane $\mathbf{Z}$.

Step 1. Write the postulate 8.

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

Step 2. Observe the diagram.

The points $A$ and $B$ are lying on the plane.

The line $AB$ joins the points $A$ and $B$ is also lying on the plane.

Step 3. Complete the given statement.

From the above diagram and postulate 8, it can be noticed that:

If there are two points $A$ and $B$ lying on the plane then the line $AB$ joining these two points $A$ and $B$ is also lying on that plane.

Therefore, the complete statement is:

If points $A$ and $B$ are in plane $Z$, then the line $AB$ will also lie on the plane $Z$.