Question

Given: ABCD is a rhombus, DPR and CBR are straight lines.

Prove that: DP × CR = DC × PR.

Answer 1

In ∆DPA and ∆RPC,

∠DPA = ∠RPC  ...(Vertically opposite angles)

∠PAD = ∠PCR  ...(Alternate angles)

∆DPA ~ ∆RPC

∴ `(DP)/(PR) = (AD)/(CR)`

`(DP)/(PR) = (DC)/(CR)`   ...(AD = DC, as ABCD is rhombus)

Hence, DP × CR = DC × PR