Constructions(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

CONSTRUCTIONS MCQs

Total Questions : 56 | Page 5 of 6 pages

Which of the following figures show the correct method to construct a triangle if we know its base, a base angle and sum of other two sides?

Discuss Question

Answer: Option A. ->

:
A

The correct procedure to construct the given triangle is:
1. Draw the base BC of $Δ$ ABC as given and construct $∠$ XBC of the required measure at B as shown.

2. Keeping the compass at point B cut an arc from the ray BX such that its length equals to AB + AC at point P and join it to C as shown.

3. Now measure $∠$ BPC and from C draw an angle equal to $∠$ BPC as shown.

Thus, option A is correct.

Question 42.

Choose the correct statemet(s) about the below construction of $60^{\circ}$ using ruler and compass.

AB = AC
AB = BC
BC = AC
AB > AC

Discuss Question

Answer: Option A. -> AB = AC
:
A, B, and C

For constructing an angle of 60 $^{\circ}$ , we draw an arc of arbitrary radius from A cutting the base of the angle at C. From C we draw another arc of the same radius cutting the previous arc at B. Since, B and C are on arcs of same radii centred at A, AB = AC.
Also, B is on arc centred at C having the same radius, so, BC = AC. So, AB = BC = AC.

Question 43.

The steps to draw a triangle with the base BC, a base angle $∠$ B and the difference of other two sides is given below.
1. Draw the base BC and at point B make an angle say XBC equal to the given angle.
2. Cut the line segment BD equal to AB - AC on the reflection of ray BX (i.e. BX').
3. Join DC and draw the perpendicular bisector, say PQ of DC.
The next step will be:

Let PQ intersect BX at a point A. Join AC.
Draw angle bisector of $∠$ C
Draw perpendicular bisector of AD
Draw angle bisector of $∠$ A

Discuss Question

Answer: Option A. -> Let PQ intersect BX at a point A. Join AC.
:
A

The next step is:
4. Let PQ intersect BX at a point A. Join AC. $Δ$ ABC is the required triangle. The construction is shown in the image below.

Question 44.

If AE = BE, then CD is the perpendicular bisector of line segment AB.

True
False
Median
Altitude

Discuss Question

Answer: Option B. -> False
:
B

The perpendicular bisector is a line that divides a line segment into two equal parts and also makes a right angle with the line segment. Here CD divides AB into two equal parts but is not perpendicular to it. Hence it is not a perpendicular bisector.

Question 45.

With a ruler and compass which of the following angles cannot be constructed?

$80^{\circ}$
$60^{\circ}$
$90^{\circ}$
$105^{\circ}$

Discuss Question

Answer: Option A. ->

80^{\circ}

:
A

With a ruler and compass we can construct $15^{\circ}$ , $30^{\circ}$ , $45^{\circ}$ , $60^{\circ}$ , $90^{\circ}$ , $105^{\circ}$ angles. We cannot construct $80^{\circ}$ .

Question 46.

For making an angle of 105 $^{\circ}$ , you need to construct a 60 $^{\circ}$ angle too.

True
False
Draw perpendicular bisector of AD
Draw angle bisector of $∠$ A

Discuss Question

Answer: Option A. -> True
:
A
A 105

^{\circ}

angle can be constructed by drawing a bisector between 120

^{\circ}

angle arm and 90

^{\circ}

arm as shown in the figure below. But it can be seen clearly that for making 120

^{\circ}

and 90

^{\circ}

angles, one needs to make a 60

^{\circ}

angle first. In the image given,

∠

DAB will be 60

^{\circ}

For Making An Angle Of 105∘, You Need To Construct A 60∘...

Question 47.

A 40° angle is obtained by drawing an angle bisector for a given 80° angle.

True
False
Cannot be determined
None of the above

Discuss Question

Answer: Option A. -> True
:
A
An angle bisector divides a given angle into two equal halves. So bisecting a given

80^{\circ}

angle will give two

40^{\circ}

angles. Hence, the given statement is true.

Question 48.

For constructing an angle of $60^{\circ}$ , we need to draw __ arc/arcs.

Discuss Question

Answer: Option A. -> True
:

We need to draw just 2 arcs to draw a $60^{\circ}$ angle. As shown in the figure below, the first arc should have P as a centre. The second arc should have the same radius as the first and should have B as a centre.

Question 49.

We can draw a triangle ABC in which BC is 12cm, $∠ B$ is $75^{\circ}$ and AB + AC = 6.5 cm.

True
False
Data insufficient
Cannot be determined

Discuss Question

Answer: Option B. -> False
:
B

We know that sum of the length of any two sides of a triangle must be greater than the length of the third side, but the condition in this question defies this law. So the given triangle can not be formed.

Question 50.

The steps to construct a triangle with given base angles $∠$ B and $∠$ C and BC + CA + AB, are:.
A. Draw a line segment, say XY equal to BC + CA + AB.
B. Make $∠$ LXY equal to $∠$ B and MYX equal to $∠$ C.
C. Bisect $∠$ LXY and $∠$ MYX. Let these bisectors intersect at a point A.
D. Draw perpendicular bisectors PQ of AX and RS of AY.
E. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.