Q11 - Geometry

Question

State a postulate, or part of a postulate, that justifies your answer to each exercise.

Does $\overleftrightarrow{AD}$ lie in plane M?

Step-by-Step Solution

Answer

Yes, $\overleftrightarrow{\mathbf{A}\mathbf{D}}$ lie in plane M.

Step 1. Write the postulate 6.

Postulate 6 is stated as “Through any two points there is exactly one line.”.

Step 2. Observe the diagram.

Now observing the given figure with two planes M and N, it can be seen that points that are labeled on plane M are B, A, C, and D.

Step 3. Relation between line AD and plane M.

Now, by using postulate 6, there is exactly one line $\overleftrightarrow{AD}$ passing through the points A and D. And as both the point lie in the same plane M so the line $\overleftrightarrow{AD}$ passing through these points also line in the plane M.