If $l$ || $m$ and P and Q are points on $l$ and $m$ respectively such that PQ ⊥ $l$ . PQ is extended to point R on line $n$ , which is in the same plane. If QR ⊥ $n$ , which of the following is true?

Both a and b

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l

n

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m

n

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Neither a or b

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Solution

The correct option is A Both a and b
Answer: (c) Both (a) and (b)
From given we get the following figure.

Clearly, from the given data, we see that PR is perpendicular to $l$ , $m$ , and $n$ .
$∴$ $l$ || $n$ and $m$ || $n$ .

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Similar questions

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Q. In a ΔPQR, if PQ = QR and mid-points of three sides PQ, QR and RP are L, M and N respectively. Prove that LN = MN.

Q. In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, OR, and RP respectively. Prove that LN = MN.

Q. In the adjoining figure, line k || line l || line m. Their transversals, line c and line d, cut them at points X, Y, Z and P, Q, R respectively. If l (XY) = 5, l (YZ) = 3 and l (PQ) = 5.5, find l (QR).

In the follow diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines l, m and n at points A,B,C and P,Q,R respectively as shown below. Prove that $\frac{A B}{B C} = \frac{P Q}{Q R}$ .

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If l || m and P and Q are points on l and m respectively such that PQ ⊥ l. PQ is extended to point R on line n, which is in the same plane. If QR ⊥ n, which of the following is true?

The correct option is A Both a and bAnswer: (c) Both (a) and (b) From given we get the following figure. Clearly, from the given data, we see that PR is perpendicular to l, m, and n. ∴ l || n and m || n.

If $l$ || $m$ and P and Q are points on $l$ and $m$ respectively such that PQ ⊥ $l$ . PQ is extended to point R on line $n$ , which is in the same plane. If QR ⊥ $n$ , which of the following is true?

The correct option is A Both a and b
Answer: (c) Both (a) and (b)
From given we get the following figure.

Clearly, from the given data, we see that PR is perpendicular to $l$ , $m$ , and $n$ .
$∴$ $l$ || $n$ and $m$ || $n$ .