The given figure shows two isosceles triangles ABC and DBC with common base BC. AD is extended to intersect BC at point P. Show that :

(i) △ABD ≡ △ACD.

(ii) △ABP ≡ △ACP.

(iii) AP bisects ∠BDC.

(iv) AP is perpendicular bisector of BC.

Two sides AB and BC and median AD of triangle ABC are respectively equal to sides PQ and QR and median PN of △PQR. Show that :

(i) △ABD ≡ △PQN.

(ii) △ABC ≡ △PQR.

In the following figure, AB = AC and AD = AE.

If ∠B = 50° ∠D = 66° and ∠GAC = 18°, find the measure of angles DAE, BAF and AGF.

In △ABC, AB = BC, AD ⊥ BC and CE ⊥ AB. Prove that AD = CE.