Constructions Test

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Constructions Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

Bisecting means dividing into two ______ parts.

A
Unequal

B
Equal

C
Triangular

D
None of these

Solution

$$\Rightarrow$$ "Bisect" means to divide into two equal parts.
$$\Rightarrow$$ You can bisect lines, angles, and more.
Question 2
1 / -0

A square is given and an angle of $$30^{o}$$ is drawn from one of its vertex . The figure will look like what?

A

B

C

D

Solution

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.
Question 3
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Directions For Questions

The steps for constructing an $$\angle ABC$$ of measure $$120^\circ$$ are given below in jumbled order:
1. From the point $$E$$, mark a point $$F$$ on the same arc with the same radius.
2. 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 $$D$$.
3. Draw a ray $$BC$$.
4. From point $$D$$, mark a point $$E$$ on the arc with the same radius.
5. Join $$B-F$$ and extend it to obtain ray $$BA$$

...view full instructions

The fourth step in the process is:

A
$$1$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

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.
Question 4
1 / -0

The steps of construction of an $$\angle AOB=45^{o}$$ is given in jumbled order below:
1. Place compass on intersection point.
2. Place ruler on start point and where arc intersects perpendicular line.
3. Adjust compass width to reach start point.
4. Construct a perpendicular line.
5. Draw $$45$$ degree line.
6. Draw an arc that intersects perpendicular line.
Which step comes first?

A
$$1$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

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.
Question 5
1 / -0

Directions For Questions

The steps for constructing an $$\angle ABC$$ of measure $$120^\circ$$ are given below in jumbled order:
1. From the point $$E$$, mark a point $$F$$ on the same arc with the same radius.
2. 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 $$D$$.
3. Draw a ray $$BC$$.
4. From point $$D$$, mark a point $$E$$ on the arc with the same radius.
5. Join $$B-F$$ and extend it to obtain ray $$BA$$

...view full instructions

The second step in the process is:

A
$$1$$

B
$$2$$

C
$$4$$

D
$$5$$

Solution

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.
Question 6
1 / -0

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 $$60^o$$

A
Only Step-1

B
Both Step-2 and Step-3

C
Only Step-3

D
Both Step-3 and Step-4

Solution

Step-3 is incorrect it should be written as: with the pointer at P (as center) now draw an arc of same radius that passes through O.
Question 7
1 / -0

Construct a triangle ABC, given: BC = 7 cm, AB -AC =1 cm and $$\angle ABC =45^{\circ}$$. Measure the lengths of AB and AC.

A
AB = 8.6 cm: AC = 7.6 cm

B
AB = 2.7 cm: AC = 1.7 cm

C
AB = 6.1 cm: AC = 5.1 cm

D
Data insufficient

Solution

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, $$AB= 6.1 cm, AC= 5.1 cm$$
Question 8
1 / -0

Angles to be bisected to obtain an angle of $$90^{\circ}$$ are:

A
$$60^{\circ}$$

B
$$60^{\circ}$$ and $$120^{\circ}$$

C
$$120^{\circ}$$ and $$180^{\circ}$$

D
$$0^{\circ}$$ and $$60^{\circ}$$

Solution

Angles to be bisected to obtain an angle of $$ {90}^\circ$$ are $$ {60}^\circ $$ and $$ {120}^\circ $$ as it exactly lies between these two angles.
$$\dfrac{60^\circ+ 120^\circ}2 = 90^\circ$$
Hence, option $$B$$.
Question 9
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Rearrange the following steps of constructing a triangle when the base angle say $$\angle B \,\, and \,\, \angle C$$ and its perimeter $$BC + CA + AB$$ is given:

$$1.$$ Draw perpendicular bisectors $$PQ$$ of $$AX$$ and $$RS$$ of $$AY$$.
$$2.$$ Draw a line segment, say $$XY$$ equal to $$BC + CA +AB$$.
$$3. $$ Let $$PQ$$ intersect $$XY$$ at $$B$$ and $$RS$$ intersect $$XY$$ at $$C$$. Join $$A-B$$ and $$A-C$$.
$$4.$$ Make $$\angle LXY$$ equal to $$\angle B$$ and $$\angle MYX$$ equal to $$\angle C$$.
$$5.$$ Bisect $$\angle LXY$$ and $$\angle MYX$$. Let these bisectors intersect at a point $$A$$.

A
$$1\rightarrow 3\rightarrow 5\rightarrow 4\rightarrow 2$$

B
$$2\rightarrow 4\rightarrow 5\rightarrow 1\rightarrow 3$$

C
$$5\rightarrow 4\rightarrow 3\rightarrow 2\rightarrow 1$$

D
$$2\rightarrow 3\rightarrow 5\rightarrow 4\rightarrow 1$$

Solution

Steps of constructing a triangle with given conditions are
$$i)$$ Draw a line segment, say $$XY$$ equal to $$BC + CA +AB$$.
$$ii)$$ Make $$\angle LXY$$ equal to $$\angle B$$ and $$\angle MYX$$ equal to $$\angle C$$.
$$iii)$$ Bisect $$\angle LXY$$ and $$\angle MYX$$. Let these bisectors intersect at a point $$A$$.
$$iv)$$ Draw perpendicular bisectors $$PQ$$ of $$AX$$ and $$RS$$ of $$AY$$.
$$v)$$ Let $$PQ$$ intersect $$XY$$ at $$B$$ and $$RS$$ intersect $$XY$$ at $$C$$. Join $$A-B$$ and $$A-C$$.

So, the correct sequence of given steps is
2→4→5→1→3
Option B is correct.
Question 10
1 / -0

An angle which can be constructed using a pair of compass and ruler is

A
$$20^{\circ}$$

B
$$80^{\circ}$$

C
$$60^{\circ}$$

D
$$110^{\circ}$$

Solution

An angle which can be constructed using a pair of compass and ruler is $$ {60}^{o} $$ as multiples of $${15}^{o} $$ can be drawn using a compass.