Question

Which of the following lines are parallel, and why? Use only the angles given to you.

A. n || p; Corresponding Angles Converse Postulate

B. a || j; Alternate Interior Angles Converse Theorem

C. n || p; Consecutive Interior Angles Converse Theorem

D. a || l; If two lines are parallel to the same line, then they are parallel to each other.

Picture attached.

Answer 1

a is parallel to j by the converse alternate exterior angles theorem

a is parallel to l by the converse corresponding angles postulate

So, a is parallel to l because:

In a plane, if two lines are parallel to the same line, they are parallel to each other.

Answer 2

@RH My final answer is above. I misread my handwriting.

Answer 3

Draw a line. Call it j.
Draw a line crossing j. Call this one p.
These 2 lines will form an angle - say 95 degrees in this case.

If you now draw a 2nd line crossing j, then the line will be parallel to p if it crosses j at the same angle as p such as we have with lne called n.
IOW, if the angles of p and n where they cross j are different, then p and n CAN NOT BE parallel, but if the angles are equal then p and n MUST be parallel.

Likewise, any lines drawn that cross either p or n that have the same angle as where j crosses p and n, MUST ALSO be parallel to j.

Answer 4

So the correct answer is B or D ? I am confused...

Answer 5

This is what I would choose: D. a || l; If two lines are parallel to the same line, then they are parallel to each other.