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Δ ABC and ΔABD are on a common base AB, and AC = BD and BC = AD as shown in

Fig. 18. Which of the following statements is true?

(i) ΔABC ≅ ΔABD

(ii) ΔABC ≅ ΔADB

(iii) ΔABC ≅ ΔBAD

Answer:

In ΔABC and ΔBAD we have,

AC = BD (given) BC = AD (given)

And AB = BA (corresponding parts of congruent triangles)

Therefore by SSS criterion of congruency, ΔABC ≅ ΔBAD

Therefore option (iii) is true.

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