SOLUTION: If 2 Parnell lines are intersected by a transversal prove that bisector of interior angle on same side of transversal intersects each other at right angle

Question 1119816: If 2 Parnell lines are intersected by a transversal prove that bisector of interior angle on same side of transversal intersects each other at right angle
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

Angle FAH = angle ECH (corresponding angles are equal)
Also, (angle ECH) + (angle ACE) = 180 degrees (supplementary angles add to 180)
Therefore (angle FAH) + (angle ACE) = 180 degrees (by simple substitution of angle FAH for angle ECH)
(angle ACB) + (angle ABC) + (angle BAC) = 180 degrees (sum of angles of triangle = 180)
But, we have:
(angle BAC) = (1/2)(angle FAH) and
(angle ACB) = (1/2)(angle ACE)
by construction of the respective angle bisectors.

Therefore
[ (1/2)(angle ACE) + (1/2)(angle FAH) ] + (angle ABC) = 180
[ (1/2) ( (angle ACE) + (angle FAH) ) ] + (angle ABC) = 180
[ (1/2)(180) ] + (angle ABC) = 180
(angle ABC) = 90 degrees (DONE)
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EDIT 7/15: Corrected contents of [ ] to have (1/2) (angle FAH). Hope the proof makes more sense now.
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