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 with two base 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∘.