Question

Direction: True or False

Answer 1

Answer:

False Any three points are always coplanar

False Two points are always collinear

False Two planes intersect at a point

Read explanations, as the answer to these questions, is subjective.

Step-by-step explanation:

The definition of coplanar is; figures that exist on the same plane. Any three points might not always be colinear, as some points might exist on one plane, but other points could exist on other planes. To visualize this phenomenon, refer to the attached image. Two points could be on the red plane, but the third could be on the green. Therefore, while there are three points, not all of them exist on the same plane. However, another plane can be constructed to connect these points, bear in mind certain problems might specifically indicate that three points are not coplanar, therefore, the answer is false.

The definition of collinear is existing on the same line. This statement is a little subject, it can be both true and false depending on the way one looks at it. A line can be drawn to connect any two points, one only needs two points to determine a line. So technically two points are always collinear. However, it also depends on the circumstance. Certain geometry problems might specifically indicate that two points are not collinear. Thus, it really depends on the context. Therefore, the answer is technically false.

Two planes usually intersect on a line. To understand this, please refer to the image attached. Tehcnailly, if a corner of one plane intersects another, then one can state that the plane intersects on a point, but typically, planes intersect on lines. Therefore, technically the answer to this problem is false, as two planes usually intersect on a line.

Images credits: Geogebra

Answer 2

9514 1404 393

Answer:

1. True
2. True
3. False

Step-by-step explanation:

1. Any three points are always coplanar. If they are collinear, then an infinite number of planes may contain the points. If they are not, then exactly one plane will contain all three points.

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2. Two points uniquely define a line, so are always collinear.

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3. Two parallel planes will not intersect at any points. Two unique non-parallel planes will intersect at a line. Two coincident planes will intersect at every one of their points. It is not possible for two planes to intersect at exactly one point.