We have proved that ∠ADB=∠BCA and ∠DAB=∠CBA based on the given information.
To prove that ∠ADB=∠BCA and ∠DAB=∠CBA, we can use the information provided:
AD=BC and BD=CA.
Here's the proof:
Given:
AD=BC
BD=CA
To Prove:
∠ADB=∠BCA
∠DAB=∠CBA
Proof:
Since AD=BC and BD=CA, we can conclude that triangles ADB and BCA are congruent by the Side-Side-Side (SSS) congruence criterion.
Therefore, ∠ADB=∠BCA (corresponding angles of congruent triangles).
Similarly, ∠DAB=∠CBA (corresponding angles of congruent triangles).
Conclusion:
∠ADB=∠BCA
∠DAB=∠CBA
Hence, we have proved that ∠ADB=∠BCA and ∠DAB=∠CBA based on the given information.
Question
In the figure AD = BC and BD = CA. Prove that ∠ADB=∠BCA and ∠DAB=∠CBA.