ABCD is a rhombus. DPR and CBR are straight lines.

Prove that:

DP.CR=DC.PR

Solution:

DP.CR=DC.PR

Given ABCD is rhombus .

DPR and CBR are straight lines.

∴ AD||CR

we need to Prove : DP.CR=DC.PR

In ∆ ADP and ∆ PCR

We have :

∠ APD = ∠ CPR

∠ ADP = ∠ PRC

∠ DAP = ∠ PCR

∴ ∆ ADP and ∆ PCR are similar triangle .

∴ we can write

AD/DP=CR/PR

Or AD.PR = DP.CR

∴ DC .PR = DP.CR Proved

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