Basic constructions

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)

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 6 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 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 first 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 second step :

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

Question 9 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 10 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 11 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 12 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 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 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 14 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 15 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 16 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 $Q$

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

Question 17 Multiple Choice (Single Answer)

With ruler and compasses,we can bisect any given line segment.

True
False

Question 18 Multiple Choice (Single Answer)

$A B C$ is a triangle. The bisectors of the internal angle $\angle B$ and external angle $\angle C$ intersect at $D.$ if $\angle B D C = 60 ^ { \circ }$ then $\angle A$ is

$120 ^ { \circ }$
$180 ^ { \circ }$
$60 ^ { \circ }$
$150 ^ { \circ }$

Question 19 Multiple Choice (Single Answer)

The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3) Find the values of x and y

15, 6
33, 12
5, 0
14, 6
none of these

Question 20 Multiple Choice (Single Answer)

If $PQ$ is the perpendicular bisector of $AB$, then $PQ$ divides $AB$ in the ratio:

$1:2$
$1:3$
$2:3$
$1:1$

Question 21 Multiple Choice (Single Answer)

For drawing the perpendicular bisector of $PQ$, which of the following radii can be taken to draw arcs from $P$ and $Q$?

$\dfrac{PQ}2$
$\dfrac{PQ}3$
$\dfrac{2PQ}3$
$\dfrac{PQ}4$

Question 22 Multiple Choice (Single Answer)

The instrument in the geometry box having the shape of a triangle is called a

Protractor
Compasses
Divider
Set-square

Question 23 Multiple Choice (Single Answer)

With compasses and ruler, construct with each of the following angles:

60 $ ^{\circ} $
30 $ ^{\circ} $
90 $ ^{\circ} $
45 $ ^{\circ} $
22 $\frac{1}{2} ^{\circ} $
75 $ ^{\circ} $

Question 24 Multiple Choice (Single Answer)

State True or False:

An angle of $52.5$ can be constructed using the compass.

True
False

Questions