SOLUTION: given: ad is perpendicular bisector of ce cd is congruent ae prove: cd is parallel ae

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Question 1018591: given: ad is perpendicular bisector of ce
cd is congruent ae
prove: cd is parallel ae
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Let m be the midpoint of ad and ce.
.
.
.
.
.
.
.
Then,


Using the Pythagorean theorem,


Substituting,

So then,


.
.
.
Look at the continuation of the red and black lines to the left of point .
That angle H is equal to angle G because by trigonometry,


and

So,


So when corresponding angles (G,H) are equal (from geometry), the lines are parallel.
So is parallel to
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