Question

∆PQR and ∆XYZ are such thatPQ//XY ,PR//XZ and PQ=XY. If PR=XZ then show that ar(∆PQR)=ar(∆XYZ)

Answer 1

In tri PQR and tri XYZ
PQ = XY  ( gn)
PR= XZ  ( gn)
angle RPQ = angle ZXY   ( corresponding angles since XY is parallel to XZ)
​PQR is congruent to XYZ
thus ar PQR = ar XYZ

Answer 2

Thank you for asking this question. Here is your answer:

PQ || XY and PQ = XY

PR || XZ and PR = XZ

Taking Δ PQR and ΔXYZ

PQ =  XY

PR = XZ

∠ QPX = ∠YXM = a

∠ RPX = ∠ZXM

∠XYZ = ∠YXM + ∠ZXM = a + b

∠XYZ = ∠QPR = a + b

ΔPQR ≅ ΔXYZ (SAS)

ar (ΔPQR)  = ar. (Δ XYZ)

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