Construction of Perpendicular Lines - Class VIII

Question 1 Multiple Choice (Single Answer)

$\overset \leftrightarrow{PQ}$ is perpendicular to $\overset \leftrightarrow{RS}$ is symbolically written as

$\overset \leftrightarrow{PQ}, \perp , \overset \leftrightarrow{RS}$
$\overset \leftrightarrow{PQ}, \parallel , \overset \leftrightarrow{RS}$
$\overset \leftrightarrow{PQ}, \neq , \overset \leftrightarrow{RS}$
$\overset \leftrightarrow{PQ}, = , \overset \leftrightarrow{RS}$

Question 2 Multiple Choice (Single Answer)

When two line segments meet at a point forming right angle they are said to be __________ to each other.

Parallel
Perpendicular
Equal
None of the above

Question 3 Multiple Choice (Single Answer)

$\displaystyle \overleftrightarrow {PQ}$ is perpendicular to $\displaystyle \overleftrightarrow {RS}$ is symbolically written as:

$\displaystyle \overleftrightarrow {PQ}\perp \overleftrightarrow {RS}$
$\displaystyle \overleftrightarrow {PQ}\parallel \overleftrightarrow{RS}$
$\displaystyle \overleftrightarrow {PQ}\neq \overleftrightarrow{RS}$
$\displaystyle \overleftrightarrow{PQ}= \overleftrightarrow {RS}$

Question 4 Multiple Choice (Single Answer)

When two lines are perpendicular to each other, the angle is said to be _______ angle.

acute
right
obtuse
equal

Question 5 Multiple Choice (Single Answer)

A perpendicular is drawn using

scale
scale protractor
set square
divider

Question 6 Multiple Choice (Single Answer)

When a perpendicular is drawn to a given line, in what ratio is the line divided into?

$1:1$
$1:2$
$2:1$
Cannot be said

Question 7 Multiple Choice (Single Answer)

The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the fourth step :

$1$
$2$
$3$
$4$

Question 8 Multiple Choice (Single Answer)

The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the first step :

$1$
$2$
$3$
$4$

Question 9 Multiple Choice (Single Answer)

The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the second step :

$1$
$2$
$3$
$4$

Question 10 Multiple Choice (Single Answer)

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the first step from the following.
1) Draw line $PQ$.
2)Draw a line $L$ and consider point $P$ outside the line.
3)Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.

$4$
$3$
$2$
$1$

Question 11 Multiple Choice (Single Answer)

When a perpendicular is drawn to a given line and it also bisects it, then the perpendicular divides the line into

$1:1$
$1:2$
$2:3$
None of the above

Question 12 Multiple Choice (Single Answer)

The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the third step :

$1$
$2$
$3$
$4$

Question 13 Multiple Choice (Single Answer)

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the third step from the following.
1) Draw line $PQ$.
2)Draw a line $L$ and consider point $P$ outside the line.
3)Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.

$4$
$3$
$2$
$1$

Question 14 Multiple Choice (Single Answer)

To construct a perpendicular to a line ($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the second step from the following.
1)Draw line $PQ$.
2)Draw a line $L$ and consider point $P$ outside the line.
3)Take $P$ as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively.
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the plane.The point where these arcs intersect name that point as $Q$.

$4$
$3$
$2$
$1$

Question 15 Multiple Choice (Single Answer)

There is a rectangular sheet of dimension $(2m-1)\times (2n-1)$, (where $m > 0, n > 0$). It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length?

$(m+n+1)^2$
$mn(m+1)(n+1)$
$4^{m+n-2}$
$m^2n^2$

Question 16 Multiple Choice (Single Answer)

The steps for constructing a perpendicular from point $A$ to line $PQ$ is given in jumbled order as follows: $(A$ does not lie on $PQ)$

1. Join $R-S$ passing through $A$.

2. Place the pointed end of the compass on $A$ and with an arbitrary radius, mark two points $D$ and $E$ on line $PQ$ with the same radius.

3. From points $D$ and $E$, mark two intersecting arcs on either side of $PQ$ and name them $R$ and $S$.

4. Draw a line $PQ$ and take a point $A$ anywhere outside the line.

The second step in the process is:

$1$
$2$
$3$
$4$

Question 17 Multiple Choice (Single Answer)

To construct a perpendicular to a line($L$) from a point ($P$) outside the line, steps are given in jumbled form.Identify the fourth step from the following
1) Draw line $PQ$
2)Draw a line $L$ and consider point $P$ outside the line
3)Take P as a center, draw $2$ arcs on line $L$ and name it as points $A$ and $B$ respectively
4)Taking $A$ and $B$ as a center one by one and keeping the same distance in compass, draw the arcs on other side of the line.The point where these arcs intersect name that point as $Q$

$4$
$3$
$2$
$1$

Construction of Perpendicular Lines - Class VIII

Questions