Question

1. If E and Fare points on the sides PQ and PR respectively of a triangle PQR for the
following case state whether EF||QR.
PE= 4cm, QE=4.5cm, PF=8cm & RF=9cm​

Answer 1

GivEn:-

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

To Show:-

• EF||QR

SoluTion:-

We know,

☯ $\sf {\red{\underline{Triangle \;Proportionality \;Theorem\; -}}}$

• If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

★ So, if the lines EF and QR are two be parallel, then ratio PE:EQ should be proportional to PF and FR.

Here,

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

Therefore,

$\dashrightarrow\sf \dfrac{PE}{EQ} = \dfrac{4}{4.5}$

And

$\dashrightarrow\sf \dfrac{PF}{FR} = \dfrac{8}{9}$

$\dashrightarrow\sf \dfrac{PF}{FR} = \dfrac{PE}{EQ}$

$\dashrightarrow\sf \dfrac{4}{4.5} = \dfrac{8}{9}$

$\therefore\;\sf {\underline{\purple{EF\;||\;QR.}}}$

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Answer 2

Answer:

PE / QE = 4 / 4.5 = 8 / 9

PF / RF = 8 / 9

PE / QE = PF / RF

Therefore, by converse of basic proportionality theorem, EF parallel to QR.