MCQ Questions for Class 9 Maths Constructions Quiz 1

For constructing a triangle when the base, one base angle and the difference between lengths of other two sides are given, the base length is equals to:

0%
The difference between lengths of other two sides
0%
The given base length
0%
The largest side
0%
None of these

The first step in the process is:

0%
$1$
0%
$2$
0%
$3$
0%
$4$

Explanation

Correct sequence is :

Step 1. Draw a ray $BC$ .

Step 2. With the pointed end of the compass at B and any arbitrary radius, draw an arc and mark the intersection point with ray $BC$ as $D.$

Step 3. With the same radius and the pointed end of the compass at $D$ , mark a point $E$ on the same arc.

Step 4 Join $B−E$ and extend it as a ray $BA.$

So the first step is $2$

Option $B$ is correct.

You are asked to "construct" an angle whose measure is

$30^\circ$ . Which of the following methods would be considered as an acceptable construction?

0%
Using a compass and straightedge, construct two parallel lines and label one of the angles $30^\circ$ .
0%
Using a compass and straightedge, construct an equilateral triangle and then bisect one of its angles.
0%
Using a compass and straightedge, copy an angle that appears to be close to $30^\circ$ from a diagram in your textbook.
0%
None of these

Explanation

We only need to construct an angle of

$30^{o}$ .

We have not been provided with any side or point.

So, its best to construct an equilateral triangle by drawing

$60^{\circ}$ angles and then extending and joining them with the straighedges

Since every angle is of measure

$60^{o}$ , so bisecting one of the angle will form an angle of measure

$30^{o}$ .

Hence, the acceptable construction is given by option B.

Construct a

$\triangle ABC$ in which

$AB= 5.4\ cm, \angle CAB= 45^{\circ}$ and

$AC + BC= 9\ cm.$ Then,

$m\angle ACB$ is:

0%
$55^o$
0%
$75^o$
0%
$85^o$
0%
None of these

Which of the following angles is possible to construct using a compass?

0%
$60^\circ$
0%
$32^\circ$
0%
$51.25^\circ$
0%
$49^\circ$

Explanation

An angle of

$60^{\circ}$ can be constructed using a compass.

Step 1 : Make a compelete arc on a straight line.

Step 2 : Make an arc on the previous arc with the same opening of compass from the start point of previous arc.

Step 3: Draw a line through the centre of arc and point of intersection.

Which diagram below shows a correct mathematical construction using only a compass and a straightedge to bisect an angle?

For constructing a triangle whose perimeter and both base angles are given, the base length is equal to:

0%
the length of the perimeter
0%
the length of the largest side
0%
the difference between the largest and the shortest side
0%
None of these

The last step in the process is:

0%
$1$
0%
$2$
0%
$4$
0%
$5$

Explanation

Correct sequence is

Step 1. Draw a ray

$QR$

Step 2. Place the pointed end of the compass on

$Q$ and draw a semi circular arc with arbitrary radius.

Step 3.Mark a point

$B$ on the same arc with the same radius from point

$A$ . Similarly , mark a point

$C$ from

$B.$

Step 4. Draw two intersecting arcs from

$B$ and

$C$ and mark the intersection as point

$D$ .

Step 5. Join

$Q-D$ and extend it to obtain

$QP.$

So the last step is

$2$

Option

$B$ is correct.

The steps of construction of an

$\angle AOB=45^{o}$ is given in jumbled order below:
1. Place compass on intersection point.
Place ruler on start point and where arc intersects perpendicular line.
Adjust compass width to reach start point.
Construct a perpendicular line.
Draw

$45$ degree line.
Draw an arc that intersects perpendicular line.
The third step in process is:

0%
$2$
0%
$3$
0%
$4$
0%
$5$

Each angle of equilateral triangle is

$60^\circ$ . The angles are bisected then each angle will be of:

0%
$60^o$
0%
$30^o$
0%
$90^o$
0%
$120^o$

Explanation

Angle bisector divide the angle in two equal parts.

$\therefore$ bisected angle

$=\dfrac{60^{\circ}}{2}=30^{\circ}$

So option

$B$ is correct.

An architect needs a staircase attached to a wall.The angle between stair and ground needs to be 30.
His plan will look like:

Explanation

Only option

$(B)$ shape have an angle equivalent to

$30^o$ .

So architect plan will look like shape

$(B)$ .

1365474_637709_ans_d6273a870f694c7dbe4fa30e8f77b6d3.png

The steps for constructing an

$\angle ABC$ of measure

$120^\circ$ are given below in jumbled order:
From the point

$R$ , mark a point

$P$ on the same arc with the same radius.
Place the pointed end of the compass on

$B$ and draw a semi-circular arc with arbitrary radius and name its intersection with ray

$BC$ as

$Q$ .
Draw a ray

$BC$ .
From point

$Q$ , mark a point

$R$ on the arc with the same radius.
Join

$B-P$ and extend it to obtain ray

$BA$

$The \ fifth \ step \ in \ the \ process \ is:$

0%
$2$
0%
$3$
0%
$4$
0%
$5$

Explanation

Correct sequence is :

Step 1. Draw a ray

$BC$ .

Step 2.Place the pointed end of the compass on

$B$ and draw a semi-circular arc with arbitrary radius and name its intersection with the ray

$BC$ as

$Q$ .

Step 3. From

$Q$ mark a point

$R$ on the arc with the same radius.

Step 4. From point

$R$ , mark a point

$P$ on the same arc with same radius.

Step 5. Join

$B-P$ and extend it to obtain ray

$BA$

So the fifth step is

$5$

Option

$D$ is correct.

Bisecting means dividing into two ______ parts.

0%
Unequal
0%
Equal
0%
Triangular
0%
None of these

Explanation

$\Rightarrow$ "Bisect" means to divide into two equal parts.

$\Rightarrow$ You can bisect lines, angles, and more.

The fourth step in the process is:

0%
$1$
0%
$3$
0%
$4$
0%
$5$

Explanation

Correct sequence is :

Step 1. Draw a ray

$BC$ .

Step 2.Place the pointed end of the compass on

$B$ and draw a semi-circular arc with arbitrary radius and name its intersection with the ray

$BC$ as

$D$ .

Step 3. From

$D$ mark a point

$E$ on the arc with the same radius.

Step 4. From point

$E$ , mark a point

$F$ on the same arc with same radius.

Step 5. Join

$B-F$ and extend it to obtain ray

$BA$

So the fourth step is

$1$

Option

$A$ is correct.

A square is given and an angle of

$30^{o}$ is drawn from one of its vertex . The figure will look like what?

Explanation

Place a protractor and draw an angle of

$30^{\circ}$ on one of its vertex.

If angle is drawn on the topmost right vertex then the figure looks like figure in option

$D$

So option

$D$ is correct.

The steps of construction of an

$45$ degree line.
Draw an arc that intersects perpendicular line.
Which step comes first?

0%
$1$
0%
$3$
0%
$4$
0%
$5$

Explanation

Correct sequence is :

1. Construct a perpendicular line .

2. Draw an arc that intersect the perpendicular line.

3. Adjust the compass width to reach the start point .

4.Place compass on intersection point.

5. Place ruler on start point and where the arc intersects the perpendicular line.

6. Draw

$45$ degree line.

So the first step is

$4$

Option

$C$ is correct.

The second step in the process is:

0%
$1$
0%
$2$
0%
$4$
0%
$5$

Explanation

Correct sequence is :

Step 1. Draw a ray

$BC$ .

Step 2.Place the pointed end of the compass on

$B$ and draw a semi-circular arc with arbitrary radius and name its intersection with the ray

$BC$ as

$D$ .

Step 3. From

$D$ mark a point

$E$ on the arc with the same radius.

Step 4. From point

$E$ , mark a point

$F$ on the same arc with same radius.

Step 5. Join

$B-F$ and extend it to obtain ray

$BA$

So the second step is

$2$

Option

$B$ is correct.

Which of the following steps is INCORRECT while constructing an angle of

$60^o$ ?
Step-1: Draw a line EF and mark a point O on it.
Step-2: Place the pointer of the compass at O and draw an arc of convenient radius which cuts the line EF at point P.
Step-3 : With the pointer at A (as center) now draw an arc that passes through O.
Step-4: Let the two arcs intersect at Q. Join OQ. We get

$\angle$ QOP whose measure is

$60^o$

0%
Only Step-1
0%
Both Step-2 and Step-3
0%
Only Step-3
0%
Both Step-3 and Step-4

Construct a triangle ABC, given: BC = 7 cm, AB -AC =1 cm and

$\angle ABC =45^{\circ}$ . Measure the lengths of AB and AC.

0%
AB = 8.6 cm: AC = 7.6 cm
0%
AB = 2.7 cm: AC = 1.7 cm
0%
AB = 6.1 cm: AC = 5.1 cm
0%
Data insufficient

Explanation

Step 1 : Draw a line segment BC of length

$7 cm$
Step 2 : Draw an angle of

${45}^{o}$ from point B

Step 3 : From Ray AX cut off the line segment

$BD = 1 cm$
Step 4 : Join C to D
Step 5 : Draw side bisector of DC
Step 6 : Extend side bisector of DC it intersect the Ray BX at point A
Step 7 : Join A to C, ABC is the required triangle.
On measuring,

$AB= 6.1 cm, AC= 5.1 cm$

With the help of a ruler and a compass it is not possible to construct an angle of.

0%
$37.5^{\circ}$
0%
$40^{\circ}$
0%
$22.5^{\circ}$
0%
$67.5^{\circ}$

Explanation

${\textbf{Step -1: Find angle by ruler and compass}}$

$\angle {37.5^ \circ }{\text{can be constructed by bisecting }} {150^ \circ } {\text{twice which can be done by compass}}.$

$\angle {22.5^ \circ }{\text{is the bisector of }}{90^ \circ }{\text{ which can be also constructed using compass}}{\text{.}}$

$\angle {67.5^ \circ }{\text{is the bisector of }} {135^ \circ } {\text{which can also be drawn using compass}}{\text{.}}$

${\textbf{Step -2: Find 40}^{\circ} {\textbf{why not done by ruler}}}$

${\text{But }}40^ \circ {\text{can not be drawn using ruler and compass}}{\text{.}}$

${\textbf{Hence, option B is correct}}{\text{.}}$

CBSE Questions for Class 9 Maths Constructions Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Constructions Quiz 1 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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