In triangle PQR, QD is the median of side PR and QD os produced to E, such that QD=DE. Prove that PE is parallel to QR.
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Given : In triangle PQR, QD is the median of side PR and QD os produced to E, such that QD=DE
To find : Prove that PE is parallel to QR.
Solution:
QD is the median of side PR
=> DR = DP
QD = DE given
∠RDQ = ∠PDE ( vertically opposite angle)
=> Δ RDQ ≅ Δ PDE
=>
∠RQD = ∠ PED
=> ∠RQE = ∠PEQ
=> PE ║ QR
QED
Hence proved
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