Given: ABCD is a rhombus, DRP and CBR are straight lines. Prove t… - Vidyadip

Question

Given: ABCD is a rhombus, DRP and CBR are straight lines.

Prove that:
$DP \times CR = DC \times PR$

✓

Answer

In $\triangle DPA$ and $\triangle RPC,$
$\angle DPA = \angle RPC$ (Vertically opposite angles)
$\angle PAD = \angle PCR$ (Alternate angles)
$\triangle DPA \sim \triangle RPC$
$\therefore \frac{ DP }{ PR }=\frac{ AD }{ CR }$
$\frac{ DP }{ PR }=\frac{ AD }{ CR }$
(AD = DC, as ABCD is rhombus)
Hence, $DP \times CR = DC \times PR$

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