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Given: ∠D ≅ ∠C and ∠CAB ≅ ∠DBA. Prove ΔABC ≅ ΔBAD

Given: ∠D ≅ ∠C and ∠CAB ≅ ∠DBA. Prove ΔABC ≅ ΔBAD-example-1
User Jaka Konda
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1 Answer

16 votes
16 votes

To prove that


\Delta ABC\cong\Delta BAD

We have to prove that they share at least 2 angles.

1.


\angle D\cong\angle C

This is a given fact.

2.

Notice that


\Delta ADE\cong\Delta\text{BEC}

Since they already share two angles: DEA and CEB (They are vertically opposite)

This way, we can conclude that:


\angle DAE\cong\angle\text{CBE}

In other words, the two angles on top of A and B are equal.

Therefore, we can conclude that


\angle DAB\cong\angle CBA

And since ΔABC and ΔBAD share two of their angles, we can conclude that they also share their third and that:


\Delta ABC\cong\Delta BAD

Q.E.D

User SausageFingers
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