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.
–
Yatin Khanna
·
4 months, 3 weeks ago

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AB=AC and DA=DC
–
Mithil Shah
·
4 months, 3 weeks ago

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you haven't specified which sides are equal in these isosceles triangles
–
Akarsh Jain
·
4 months, 3 weeks ago

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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. – Yatin Khanna · 4 months, 3 weeks ago

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AB=AC and DA=DC – Mithil Shah · 4 months, 3 weeks ago

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you haven't specified which sides are equal in these isosceles triangles – Akarsh Jain · 4 months, 3 weeks ago

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– Mithil Shah · 4 months, 3 weeks ago

AB=AC and DA=DCLog in to reply