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Chapter 1: Q12 (page 24)

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

Does plane N contain any points not on AB鈫�?

Short Answer

Expert verified

Yes, plane N contains any points not on AB鈫�.

Step by step solution

01

Step 1. Write the postulate 6.

Postulate 6 is stated as 鈥淭hrough any two points there is exactly one line.鈥�.

02

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.

03

Step 3. Relation between line AB and plane N.

A given plane consists of an infinite number of points and lines.

So, plane N contains a lot of points that are not on AB鈫�.

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Most popular questions from this chapter

Sketch and label the figures described. Use dashes for hidden parts.

A vertical plane intersects two horizontal planes in lines I and n.

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Theorem 1-1 states that two lines intersect at exactly one point. The diagram suggests what would happen if you tried to show two 鈥渓ines鈥� drawn through two points. State the postulate that makes this situation impossible.

State whether it is possible for the figure described to exist. Write yes or no.

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