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Throuth A,B and C lines RQ, PR and QP have been drawn, respectively parallel to sides BC. CA and AB of a `DeltaABC` as shown in the given figure. Show that `BC=1/2QR.` |
Answer» Given : Tringles ABC and PQR in which `AB "||"QP,BC"||"RQ and CA"||"PR.` To prove : `BC=1/2QR` `"Proof: Since" RA"||"BC and BR"||"CA" "("given")` `therefore"Quadrilateral RBCA is a parallelogram."" "("pair of opposite sides are parallel")` `therefore" "RA=BC" "(because"opposite sides of a parallelogram")...(1)` Now, quadrilateral ABQA is a parallelogram. `therefore" "AQ=BC" "(because"opposite sides of a parallelogram")...(2)` Adding (1) and (2), we get `" "RA+AQ=2BC` `implies" "QR=2BC` `implies" "BC=1/2QR` |
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