# Free Constructions 02 Practice Test - 9th Grade

### Question 1

A 75∘ angle can be made by drawing angle bisector between a 90∘ angle arm and a

#### SOLUTION

Solution :75∘=90∘+60∘2

Hence bisecting 90∘ and 60∘ will give 75∘.

### Question 2

In the figure shown below, ∠ABD = ∠DBC, then the ray BD is called

Angle bisector

#### SOLUTION

Solution :A

An angle bisector divides a given angle into two equal angles. Since BD divides ∠ ABC into two equal angles, it is an angle bisector.

### Question 3

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

True

False

#### SOLUTION

Solution :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 4

Choose the correct statemet(s) about the below construction of 60∘ using ruler and compass.

AB = AC

AB = BC

BC = AC

AB > AC

#### SOLUTION

Solution :A, B, and C

For constructing an angle of 60∘, 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 5

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?

#### SOLUTION

Solution :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 6

We can draw a triangle if we know its perimeter and one base angle.

#### SOLUTION

Solution :B

To draw a triangle, we must know its perimeter along withtwobase angles. Hence the given statement is false.

### Question 7

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

#### SOLUTION

Solution :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 8

Given an angle of 60∘, it is possible to get 30∘.

True

False

#### SOLUTION

Solution :A

It is possible to get 30∘ from given angle of 60∘ by simply drawing an angle bisector. Hence the given statement is true.

### Question 9

For making an angle of 105∘, you need to construct a 60∘ angle too.

True

False

#### SOLUTION

Solution :A

A 105∘ angle can be constructed by drawing a bisector between 120∘ angle arm and 90∘ arm as shown in the figure below. But it can be seen clearly that for making 120∘ and 90 ∘ angles, one needs to make a 60∘ angle first. In the image given, ∠DAB will be 60∘ .

### Question 10

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

80∘

#### SOLUTION

Solution :A

With a ruler and compass we can construct 15∘, 30∘, 45∘, 60∘, 90∘, 105∘ angles. We cannot construct 80∘.