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ABCD is a Rhombus. DPR and CBR are straight lines. Prove that: DP.CR=DC.PR

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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Comments

  1. Replies
    1. 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.

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