AC is congruent to CD according to the definition of a midpoint.
The objective is to prove AC is congruent to CD.
It is given that C is the midpoint of AE
Hence, AC = EC by the definition of a midpoint. That is, the midpoint of a line divides the line into two halves.
Similarly, BC = DC since C is the midpoint of BD.
It is given that AE is congruent to BD.
AE ≅ BD
Divide both lines by 2.
Hence, AE ÷ 2 ≅ BD ÷ 2
AE ÷ 2 = AC or EC
and, BD ÷ 2 = BC or DC
That is, AC = DC
Hence, it is proved that AC ≅ CD
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