From the given statements, let's determine the true statements.
• Through any three collinear points, there is exactly one plane.
Collinear points are three or more points that are on same straight line. Collinear points can exist on different planes.
Therefore, this statement is FALSE.
• A segment is part of a line between two points on the line called the endpoints.
A segment can be said to be a part of a line with two endpoints.
This statement is TRUE.
• If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
Using the Parallel Postulate, we can say this statement is TRUE.
• The midpoint of a segment is equidistant from the endpoints.
The midpoint of a line segement is the middle point of the line joining the two endpoints.
Since the midpoint is at the middle, this statement is TRUE.
• If two angles are supplementary to the same angle, then the angles must be obtuse.
Supplementary angles are angles that sum up to 180 degrees.
An obtuse angle is an angle that is greater than 90 but less than 180 degrees.
If two angles are supplementary to the same angle, the angles must be congruent and they may either be obtuse or acute angles.
Therefore, this statement is FALSE.
• If two angles form a linear pair, then the angles are complementary.
Complementary angles are angles that sum up to 90 degrees.
If two angles form a linear pair, then the angles are supplementary(sum up to 180 degrees) not complementary.
Therefore, this statement is FALSE.
Therefore, the true statements are:
• A segment is part of a line between two points on the line called the endpoints.
,
• If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
,
• The midpoint of a segment is equidistant from the endpoints.
ANSWER:
• A segment is part of a line between two points on the line called the endpoints.
• If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
• The midpoint of a segment is equidistant from the endpoints.