E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR

PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

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#### Solution

PE = 4 cm, QE = 4.5 cm, PF = 8 cm, RF = 9 cm

`(PE)/(EQ) = 4/4.5=8/9`

`(PF)/(FR) = 8/9`

`(PF)/(FR)=(PE)/(EQ) `

Therefore, EF is parallel to QR

Concept: Similarity of Triangles

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