Q21 of 34 Page 252

In the given figure, C is the mid-point of AB. If ∠DCA = ∠ECB and ∠DBC = ∠EAC prove that DC = EC.

Since C is the mid-point of AB.

So, AC = BC.


Taking ΔACE and ΔBCD in consideration-


∠DBC = ∠EAC


AC = BC


Also ∠DCA = ∠ECB


Adding ∠DCE on both sides-


∠DCB = ∠ECA


So, by Angle side Angle(ASA) criteria ΔACE and ΔBCD are congruent.


And hence DC = EC (by congruency criteria).


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