Question

In Fig. 7.8, OA = OB and OD = OC. Show that (i) △ AOD ≅ △ BOC and (ii) AD || BC.

AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.

In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see Fig. 7.16). Show that △ ABC ≅ △ ABD. What can you say about BC and BD?

ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that (i) △ ABD ≅ △ BAC (ii) BD = AC (iii) ∠ ABD = ∠ BAC.