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) About Me  (Show Source):
You can put this solution on YOUR website!
Let m be the midpoint of ad and ce.
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Then,
am=dm
cm=em
Using the Pythagorean theorem,
am%5E2%2Bem%5E2=ae%5E2
cm%5E2%2Bdm%5E2=cd%5E2
Substituting,
em%5E2%2Bam%5E2=cd%5E2
So then,
ae%5E2=cd%5E2
ae=cd
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Look at the continuation of the red and black lines to the left of point a.
That angle H is equal to angle G because by trigonometry,
tan%28H%29=em%2Fam
tan%28G%29=cm%2Fdm
and
tan%28G%29=em%2Fam
So,
tan%28G%29=tan%28H%29
G=H
So when corresponding angles (G,H) are equal (from geometry), the lines are parallel.
So ae is parallel to cd