SOLUTION: Complete each statement with the word always, sometimes, or never. In a plane, two lines perpendicular to the same line are _______ parallel. If two lines are a cut by a transver

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Question 763743: Complete each statement with the word always, sometimes, or never.
In a plane, two lines perpendicular to the same line are _______ parallel.
If two lines are a cut by a transversal, corresponding angles are _____ congruent.
A transversal perpendicular to one of two parallel lines is _____ perpendicular to the other line.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

In a plane, two lines perpendicular to the same line are _______ parallel.


Two lines are perpendicular to the same line. So this means that the two
form a set of right angles. This further tells us that the same side
interior angles are supplementary, and by the converse of the same side
interior angles theorem, the two lines are parallel. So this is always true

Note: this is of course assuming the two lines are distinct
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b)


If two lines are a cut by a transversal, corresponding angles are _____ congruent.

This is only true if the two lines (excluding the transversal) are parallel.
So this is sometimes true.
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c)

A transversal perpendicular to one of two parallel lines is _____ perpendicular to the other line.

Let's make lines m and n parallel, so m || n. Now let's make line k
perpendicular to line m.
If line k is perpendicular to line m, then we have a right angle in the
interior where k and m intersect. So by the same side interior angles
theorem, the two same side interior angles are supplementary, which means
the other interior angle on the other side must be 90 degrees as well (since
90+x=180 leads to x = 90). This proves that lines k and n intersect at right
angles as well
So this is always true
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Complete each statement with the word always, sometimes, or never.

In a plane, two lines perpendicular to the same line are ___always____ parallel.
If two lines are a cut by a transversal, corresponding angles are __sometimes___ congruent (it's only true if the two lines are parallel)
A transversal perpendicular to one of two parallel lines is __always___ perpendicular to the other line.