Q9. - Geometry

Question

Apply postulates and theorems to complete the statements.

Through any two points $\underset{\mathbf{¯}}{\mathbf{?}}$.

Step-by-Step Solution

Answer

The complete statement is:

Through any two points, exactly one line can pass.

Step 1. Write the postulate 6.

Postulate 6 states that through any two points, exactly one line can pass.

Step 2. Observe the diagram.

The line $AB$ is passing through the points $A$ and $B$.

Step 3. Complete the given statement.

From the above diagram, it can be noticed that:

No line other than $AB$ can pass through the two points $A$ and $B$.

Therefore, one and only one can pass through the two points.

Therefore, the complete statement is through any two points, exactly one line can pass.