Q10 - Geometry

Question

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

Name the intersection of the planes M and N.

Step-by-Step Solution

Answer

The intersection of the planes M and N is a line $\overleftrightarrow{\mathbf{A}\mathbf{B}}$.

Step 1. Write the postulate 9.

Postulate 9 is stated as “If two planes intersect, then their intersection is a 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, and points labeled on plane N are B and A.

Step 3. State the intersection of the planes M and N.

By postulate 9, the intersection of two planes is a line.

Now observing the given figure, it can be seen that the planes M and N intersect in the line $\overleftrightarrow{AB}$.