Q177Short answer
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
Show answer
Given: (i) ABCD is a gm (ii) ∠1 = ∠2 To Prove: (i) ∠3 = ∠4 (ii) ABCD is rhombus Proof: (i) ∠1 = ∠4 ∠2 = ∠3 (alt ∠s) But ∠1 = ∠2 ∠3 = ∠4 (ii) ∠1 = ∠2 (given alt.) ∠2 = ∠3 ∠1 = ∠3 Hence CD = DA ∴ ABCD is a rhombus