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Given,
AD = BC
BD = CA
To Prove- ∠ADB = ∠BCA and ∠DAB = ∠CBA.
Proof- Let us take ∆ADB and ∆BCA into consideration .
AD = BC (Given)
BD = AC (Given)
AB = AB (Common side)
∴∆ADB ≅ ∆BCA by SSS
SSS(side-side-side) congruence states that if two triangles have all the three sides equal they are congruent.
Now , Applying CPCT( Corresponding parts of congruent triangles) which states that, If two triangles are congruent then their corresponding sides are equal , also corresponding angles too.
∠ADB = ∠BCA
Similarly , ∠DAB = ∠CBA
Hence proved.
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