Mathematics
Given : ABCD is a rhombus, DPR and CBR are straight lines.
Prove that :
DP × CR = DC × PR.
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Answer
Since, ABCD is a rhombus.
So, AD || BC.
In △DPA and △RPC,
⇒ ∠DPA = ∠RPC (Vertically opposite angles are equal)
⇒ ∠PAD = ∠PCR [Since, AD || CD and AC is transversal]
∴ △DPA ~ △RPC [By AA]
Since, corresponding sides of similar triangles are proportional we have :
⇒ ……….(1)
In rhombus all sides are equal.
∴ AD = DC
Substituting in (1) we get,
⇒
⇒ DP × CR = DC × PR.
Hence, proved that DP × CR = DC × PR.
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