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

How is AD/DP?

For two similar triangles [ADP and PCR] which angles are equal. The ratio of sides of one angle can be equal to the ratio of sides of other triangle . Please read about similar triangles , you can get this property. Hope I am able to clarify your query.