CPCTC 8. ∠sBut ∠CAB = ∠CAD∴ ∠ACD = ∠CAD∴ AD = CD| Sides opposite to equal angles of a triangle are equal∴ ABCD is a square. one ABC and other is DBC. Each answer of the exercise has been carefully compiled and developed keeping in consideration the latest CBSE syllabus. And, let ∠OAC = ∠OCA = x [Angles opposite to equal sides are equal] So, ∠AOC = 180o – 2x Also, ∠BAC = 30o + x ∠BCA = 40o + x Now, in ∆ABC ∴ AD = CB | C.P.C.T.∠ODA = ∠OBC | C.P.C.T.∴ ∠BDA = ∠DBC∴ AD || BCNow, ∵ AD = CB and AD || CB∴ Quadrilateral ABCD is a || gm.In ∆AOB and ∆AOD,AO = AO | CommonOB = OD | Given∠AOB = ∠AOD| Each = 90° (Given)∴ ∆AOB ≅ ∆AOD| SAS Congruence Rule∴ AB = ADNow, ∵ ABCD is a parallelogram and∴ AB = AD∴ ABCD is a rhombus.Again, in ∆ABC and ∆BAD,AC = BD | GivenBC = AD| ∵ ABCD is a rhombusAB = BA | Common∴ ∆ABC ≅ ∆BAD| SSS Congruence Rule∴ ∆ABC = ∆BAD | C.P.C.T.AD || BC| Opp. geometry trigonometry euclidean-geometry quadrilateral Value of