SOLUTION: Given ad and bc bisect each other at e prove Abe = dce

Question 1061065: Given ad and bc bisect each other at e prove Abe = dce
Answer by KMST(5348) (Show Source): You can put this solution on YOUR website!
If AD and BC bisect each other at E, E is the midpoint of AD,
and E is also the midpoint of BC.
AE is congruent with DE because E is the midpoint of AD.
EB is congruent with EC because E is the midpoint of BC.
Angles AEB and DEC are congruent with each other,
because they are vertical angles,
formed by the intersection of lines AD and BC at point E.
That makes triangles AEB and DEC congruent by SAS (side-angle-side),
since they have congruent angles at E,
Flanked by pairs of congruent sides.
By CPCTC (Corresponding Parts of Congruent Triangles are Congruent),
Their corresponding angles at B and C (DCE and ABE) are congruent.

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