Through a point not on a line, one and only one line can be drawn parallel to the given line. always sometimes never 10. two coplanar lines that are perpendicular to the same line are parallel. always sometimes never

The parallel postulate: In a plane there can be drawn through any point A, lying outside of a straight line a, one and only one straight line which does not intersect the line a. This straight line is called the parallel to a through the given point A.

Therefore, first statement is always true.

Coplanar lines are lines that lie on the same plane.

Theorem: If two coplanar lines are perpendicular to the same  line, then the two lines are parallel to each other.

Therefore, second statement is always true.

1st question: always

2nd question: always

Step-by-step explanation:

1st question

Given a line and a point which is not on that line, there is only one new line parallel to the old line which pass through the point. That is, there are infinity new lines parallel to the old line, but only one of them pass through the given point.

2nd question

If two coplanar lines are parallel and intercept a third line, then the same angle is formed in the interception between each parallel line and the third line. In this case a 90° angle is formed and each parallel line is perpendicular with the third line.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b