1.

Diagonal AC of a parallelogram ABCD bisects ∠A. Show that(i) it bisects ∠C also,(ii) ABCD is a rhombus.

Answer»

Data: Diagonal AC of a parallelogram ABCD bisects ∠A. 

To Prove: (i) Diagonal AC also bisects ∠C. 

(ii) ABCD is a rhombus. 

Proof: i) Diagonal AC also bisects ∠A. 

∴ ∠DAC = ∠BAC …………… (i) 

But, ∠DAC= ∠BCA (alternate angles)(ii) 

∠BAC=∠DCA (alternate angles)(iii) 

From (i), (ii) and (iii), 

∠BCA = ∠DCA 

∴ AC bisects ∠C. 

(ii) ∠DAC = ∠DCA 

∴ AD = DC 

But, AD = BC 

∴ DC = AB 

∴ AB = BC = CD = DA 

∴ ABCD is a rhombus.



Discussion

No Comment Found

Related InterviewSolutions