Q4. - Geometry

Question

Points $\mathbf{A}$ and $\mathbf{B}$ are known to lie in a plane.

1. What can you say about $\overleftrightarrow{\mathbf{A}\mathbf{B}}$?
2. State the postulate that supports your answer to part (a).

Step-by-Step Solution

Answer

1. The line $\overleftrightarrow{AB}$ lies on the plane itself.
2. The postulate that supports the answer to part (a) is postulate 8 which states that if the two points lie on the plane then the line joining those points also lies on that plane.

Part a. Step 1. Draw a plane X containing the two points A and B.

The diagram showing the plane $X$ containing the points $A$ and $B$ is:

Part a. Step 2. Draw line AB

Draw the line $AB$ by joining point $A$ to point $B$ as shown:

Part a. Step 3. Relation of line AB with the plane.

It can be noticed from the diagram that the line $AB$ joining the points $A$ and $B$ also lies on the plane.

Therefore, it can be said about the line $AB$ that the line $AB$ is also lying on the plane.

Part b. Step 1. Write the answer to part (a).

The line is also lying on the plane.

Part b. Step 2. Write the postulate 8.

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

Part b. Step 3. Name the postulate that supports the answer to part (a).

It can be noticed that:

Postulate 8 stating that if the two points lie on the plane then the line joining those points also lies on that plane supports the answer to part (a).