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Question
Given: ABCD is a rhombus, DPR and CBR are straight lines.
Prove that: DP × CR = DC × PR.
Sum
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Solution
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
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