Construct DE such that E lies on AB and angle ADC=60°. Then; ADE will be an equilateral triangle.
Then; AE=ED=DA ;
But; DA=DC
So; AE=DC............... (1)

Next; we can join EC and by some elementary angle chasing we can conclude angle BEC= angle BCE and hence;
BE=BC................ (2)

Adding (1) & (2) gives the desired result i.e. AE+BE=BC+DC or AB=BC+CD.

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## Comments

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TopNewestConstruct DE such that E lies on AB and angle ADC=60°. Then; ADE will be an equilateral triangle.

Then; AE=ED=DA ;

But; DA=DC

So; AE=DC............... (1)

Next; we can join EC and by some elementary angle chasing we can conclude angle BEC= angle BCE and hence;

BE=BC................ (2)

Adding (1) & (2) gives the desired result i.e. AE+BE=BC+DC or AB=BC+CD.

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AB=AC and DA=DC

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you haven't specified which sides are equal in these isosceles triangles

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AB=AC and DA=DC

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