Thread: parrallel line proof

Prove in a Statement and Reason Chart that


Line m and l are parallel.


Given angle 8 and 2 are alternate exteroir angles

Originally Posted by Dragon

Prove in a Statement and Reason Chart that


Line m and l are parallel.


Given angle 8 and 2 are alternate exteroir angles

We need a picture or something...

-Dan

Originally Posted by Dragon

Well, you didn't lable the angles, but there are only 2 alternate exterior angles...the are the orange angle and the angle opposite the top yellow angle.

Look at the orange and yellow angles at the bottom. They must be equal since they are vertex angles. Similarly the yellow angle at the top is equal to the other alternate exterior angle.

Since the two alternate exterior angles are equal (given) then the two yellow angles must also be equal because each yellow angle is equal to one of the alternate exterior angles.

The yellow angles are alternate interior angles. If two lines are cut by a transversal and the alternate interior angles are equal the two lines are parallel. (Euclid's 5th postulate.)

-Dan