TRIANGLE PQR AND TRIANGLE XYZ ARE SUCH THAT PQ PARALLEL TO XY, PQ = XY. IF PR= XR, THEN SHOW THAT AR(TRIANGLE PQR) = AR(TRIANGLE XYZ)
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Please find below the solution to the asked query:

Given :PQ∥XY and PQ=XYPR∥XZ and PR=XZTaking △PQR and △XYZ,PQ=XY (Given)PR=XZ (Given)∠QPX=∠YXM=a (Corresponding angles are equal as PQ∥XY)∠RPX=∠ZXM=b (Corresponding angles are equal as PR∥XZ)so, ∠XYZ=∠YXM+∠ZXM=a+bhence,∠XYZ=∠QPR=a+b so,△PQR≅△XYZ (SAS)hence,ar.(△PQR)=ar.(△XYZ) −−[congruent triangles have equal area]
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Please find below the solution to the asked query:

Given :PQ∥XY and PQ=XYPR∥XZ and PR=XZTaking △PQR and △XYZ,PQ=XY (Given)PR=XZ (Given)∠QPX=∠YXM=a (Corresponding angles are equal as PQ∥XY)∠RPX=∠ZXM=b (Corresponding angles are equal as PR∥XZ)so, ∠XYZ=∠YXM+∠ZXM=a+bhence,∠XYZ=∠QPR=a+b so,△PQR≅△XYZ (SAS)hence,ar.(△PQR)=ar.(△XYZ) −−[congruent triangles have equal area]
Hope this information will clear your doubts about this topic.
If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards
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