In the given figure , AD and CE bisect each other. Prove that AE || CD
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given : AD and CE bisect each other
to prove : AE is parallel to CD
proof : in triangle AEB and triangle BCD
AB=BD (CE bisects AD)
angle 1 = angle 2 (vertical angles)
EB=BC (AD bisects CE)
by SAS congruency
triangle AEB is congruent to triangle BCD
Angle 5= angle 4 (cpct)
but these are alternate angles
so AE is parallel to CD
Hope it helps u
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