Question

Through P, Q and R lines BC, AB and AC has been drawn respectively parallel to the sides QR, PR and PQ of a triangle PQR.  Prove that QR = ½ BC.  
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Answer 1

Step-by-step explanation:

if an object of 7 cm heght is placed at a distance of 12 cm from a convex lens of focal length 8 cm foind the position,nature and height of image

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Answer 2

Given :- Through P, Q and R lines BC, AB and AC has been drawn respectively parallel to the sides QR, PR and PQ of a triangle PQR. Prove that BC = (1/2) QR. ?

Solution :-

from image given that :-

• PQR is a ∆.
• BC || QR, AB || PQ and AC || PR.

we have given that,

→ BC || QR

So,

→ BC || RA

also,

→ AC || PR,

So,

→ AC || BR .

Therefore,

Quadrilateral RBCA is a parallelogram as pair of opposite sides are parallel .

Hence,

→ RA = BC ( opposite sides of a parallelogram ).

Similarly,

Quadrilateral ABCQ is also a parallelogram.

Than,

→ AQ = BC ( opposite sides of a parallelogram ).

from adding both result we get,

→ RA + AQ = 2BC

→ QR = 2BC

→ BC = (1/2) QR (Proved).

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3.

In the fig, AB || CD,FIND x.(Hint:Prove that AOB-COD).

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