Question

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

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.

In Fig. 7.21, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Show that BC = DE.

In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see Fig. 7.23). Show that: (i) △ AMC ≅ △ BMD (ii) ∠ DBC is a right angle. (iii) △ DBC ≅ △ ACB (iv) CM = 1/2 AB