We are given that ∠BCD ≅ ∠CDB and then, by the Converse of Isosceles Triangle Theorem, we get that the opposite sides to these angles are congruent. That is, BD≅ BC.
Next, by applying the Triangle Inequality Theorem to â–³ ABD we get three inequalities.
AB + BD &> AD
AB + AD &> BD
BD + AD &> AB
Since BD≅ BC we have that BD = BC. By substituting this into the second inequality above, we will get what we wanted to prove.
AB + AD > BC
In the following two-column table we summarize the proof we did above.
