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Given :
In triangle PQR, XY || QR ,M and N are midpoints of PY and PR .
∴ PM=MY= MN
and PY=YR
∴PY=2PM
and YR=2PM=2MN
solution :
since XY || QR
then by basic proportionality theorem:
1. proof :Δ PXM ≈ Δ PQN
In ᐃPXM and Δ PQN,
PX / XQ = PM/MN
angle P = angleP ( common )
∴ SAS similarity criteria,
Δ PXM ≈ Δ PQN
2. proof : XM || QN
since Δ PXM ≈ Δ PQN
we have ;
PX / XQ = PM / MN
by converse of BPT
XM || QN
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