Math, asked by vaibhavikhalkar59, 11 months ago

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Answered by mohitjnit
0

Answer:

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Answered by Anonymous
3

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:

 \frac{px}{xq}  =  \frac{py}{yr}

 \frac{px}{xq}  =  \frac{2pm}{2mn}

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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