Free Constructions 02 Practice Test - 9th Grade

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

SOLUTION

Solution :

75=90+602
Hence bisecting 90 and 60 will give 75.

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

A.

Angle bisector

B. Perpendicular bisector
C. Median
D. Altitude

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.

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

A.

True

B.

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.

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

A.

AB = AC

B.

AB = BC

C.

BC = AC

D.

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.

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?

A.

B.
C.
D.

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.

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

A. True
B. False
C. Not always
D. Cannot be predicted

SOLUTION

Solution : B

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

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:

A.

Let PQ intersect BX at a point A. Join AC.

B.

Draw angle bisector of C

C.

D.

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.

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

A.

True

B.

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.

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

A.

True

B.

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 .

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

A.

80

B. 60
C.  90
D. 105

SOLUTION

Solution : A

With a ruler and compass we can construct 15304560, 90105 angles. We cannot construct 80.