# parrallel line proof

• Nov 1st 2006, 06:31 AM
Dragon
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
• Nov 1st 2006, 06:43 AM
topsquark
Quote:

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
• Nov 1st 2006, 06:47 AM
Dragon
• Nov 1st 2006, 06:58 AM
topsquark
Quote:
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