Q9 - Geometry

Question

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

Name three points that determine plane M.

Step-by-Step Solution

Answer

Three points that determine plane M are B, C, and D.

Step 1. Write the postulate 7.

Postulate 7 is stated as “Through any three points there is at least one plane and through any three non-collinear points there is exactly one plane.”

Step 2. Observe the diagram.

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

Step 3. State three points that determine plane M.

By postulate 7, any three non-collinear points on the given plane can be used to determine that plane.

Now observing the given figure, it can be seen that three points that are labeled on the plane M, that are also non-collinear (do not lie on the same straight line) are B, C, and D.

So, by using postulate 7 it can be said that points B, C, and D can be used to determine plane M.