Question

ABCD is a trapizum AB parallel CD and AD=BCshow that 1.angle A=angle B 2.triangle ABC congurent Totriangle BAD​

Answer 1

Answer:

Step-by-step explanation:

Construction: Draw a line through C parallel to DAintersecting AB produced at E.Proof:i)AB||CD(given)AD||EC (by construction)So ,ADCE is a parallelogramCE = AD(Opposite sides of a parallelogram)AD = BC (Given)We know that ,∠A+∠E= 180°[interiorangles on the same side of the transversal AE]∠E= 180° - ∠AAlso, BC = CE∠E = ∠CBE= 180° -∠A∠ABC= 180° - ∠CBE[ABE  is a straight line]∠ABC= 180° - (180°-∠A)∠ABC= 180° - 180°+∠A∠B= ∠A………(i) (ii) ∠A + ∠D = ∠B + ∠C = 180° (Angles onthe same side of transversal)∠A + ∠D = ∠A + ∠C (∠A = ∠B) from eq (i) ∠D = ∠C (iii) In ΔABC and ΔBAD,AB = AB (Common)∠DBA = ∠CBA(from eq (i)AD = BC (Given)ΔABC ≅ ΔBAD (by SAS congruence rule)(iv)  Diagonal AC = diagonal BD (by CPCT as ΔABC ≅ ΔBAD)