MATH SOLVE

7 months ago

Q:
# Which of the following reasons could be used to conclude that the lines are parallel based on the given information?If right angles are formed, then lines are parallel.If two lines are perpendicular to another line, then they are parallel.If alternate interior angles are equal, then lines are parallel.

Accepted Solution

A:

We have been given three statements. From those statements, we have to pick the statement that can conclude that that two lines are parallel.

Statement 1:If right angles are formed, then lines are parallel.This is not valid because if the angle formed is right angle then lines forming right angle will be perpendicular.

Statement 2:If two lines are perpendicular to another line, then they are parallel.This is valid because the line on which other two lines are perpendicular will work as transversal and the alternet interior angles will be equal. Hence the two perpendicular lines on given line will be parallel to each other.

Statement 3:If alternate interior angles are equal, then lines are parallel.This is valid as explained above.

Hence final answer are statement 2 and statement 3 both.

Statement 1:If right angles are formed, then lines are parallel.This is not valid because if the angle formed is right angle then lines forming right angle will be perpendicular.

Statement 2:If two lines are perpendicular to another line, then they are parallel.This is valid because the line on which other two lines are perpendicular will work as transversal and the alternet interior angles will be equal. Hence the two perpendicular lines on given line will be parallel to each other.

Statement 3:If alternate interior angles are equal, then lines are parallel.This is valid as explained above.

Hence final answer are statement 2 and statement 3 both.