devarshi-dt-logo

Question:

ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.

Solution:

In△ABDand△BCD,AB=BCSides of a rhombusAD=CDSides of a rhombusBD=BDCommon side△ABD≅△BCD...SSS test of congruence∴∠ABD=∠CBDC.P.C.T.∴∠ADB=∠CDBC.P.C.T.So, DiagonalBDbisects∠Band∠Dof the rhombusABCD.Similarly we can prove,△ABC≅△ADC∴∠BAC=∠DACC.P.C.T.∴∠BCA=∠DCAC.P.C.TSo, DiagonalACbisects∠Aand∠Cof the rhombusABCD.