# Free Constructions 01 Practice Test - 9th Grade

### Question 1

In which of the following situations an angle bisector cannot be constructed to bisect the angle formed between two given lines?

#### SOLUTION

Solution :B

Since two parallel lines do not intersect each other, an angle cannot be formed between them. Thus in this case, angle bisection is not possible.

### Question 2

In which of the following quadrilaterals, a diagonal is not an angle bisector?

#### SOLUTION

Solution :B

In the case of a rectangle, the diagonal is not an angle bisector.

Consider a rectangle ABCD.

Here, ∠ ADB = ∠ DBC (Alternate angles)

But, ∠ DBC is not equal to ∠ BDC (Angles opposite to unequal sides of a triangle are unequal)

∴ ∠ ADB is not equal to ∠ BDC

So, diagonal DB does not bisect ∠ D.

### Question 3

Each point on a/an _________ is such that it forms an isosceles triangle with the end points of the given line segment.

#### SOLUTION

Solution :A

Consider the above figure.

Here, XY is the perpendicular bisector of a line AB.

Let P be any random point on XY.

In △ PMA ≅ △ PMB

AM = BM (Perpendicular bisector divides a line segment into two equal halves)

∠ PMA = ∠ PMB = 90∘

Also PM is common side

So △ PMA ≅ △ PMB (SAS Rule)

∴ PA = PB (CPCT)

Hence, △ PAB is an isosceles triangle.

So, the given statement is true.

### Question 4

For which of the following can a perpendicular bisector be drawn?

Line

Ray

Line segment

Both Line and Ray

#### SOLUTION

Solution :C

A perpendicular bisector can be drawn only if a figure has end points. Only a line segment has a definite length and hence it can be bisected by a perpendicular bisector.

### Question 5

Which among the following angles cannot be constructed just by using a ruler and a compass?

30 degrees

60 degrees

70 degrees

90 degrees

#### SOLUTION

Solution :C

All the standard angles and the angles which can be obtained by bisecting standard angles can be constructed just by using a ruler and compass. Here except 70∘ all other angles can be constructed using ruler and compass.

### Question 6

For constructing a right angle without a protractor, which of the following method/s is/are used?

Angle Bisector

60∘ angle construction

Construction of triangle

#### SOLUTION

Solution :A and B

To construct a right angle triangle, the following steps should be followed:

1. Draw a line OB of given length.

2. With O as centre, make an arc of any radius intersecting OB at X.

3. With X as a centre, draw another arc keeping the radius same intersecting the previous arc at D.

4. ∠DOB will be 60∘.

5. With D as a centre and keeping the radius same, draw another arc intersecting the first arc at C.

6. ∠COB will be 120∘ .

7. Bisect COD drawing two equal arcs from each points intersecting at E.

8. Join EO and extend till A. ∠AOB will be 90∘.

So, it can be seen that both 60∘ and angle bisector construction is used in the process.

### Question 7

Two sides of a triangle have lengths of 5 units and 6 units respectively. Which of the following is a possible length for the third side?

11

12

13

10

#### SOLUTION

Solution :D

In a triangle, the sum of the lengths of any 2 sides of a triangle must be greater than the third side. The third side can measure anything less than 11 units. Hence, the third side can be 10 units.

### Question 8

For constructing a triangle with a given base, a base angle and difference between the other two sides, a

#### SOLUTION

Solution :The procedure for Triangle Construction 2 is:

1. Draw the base BC of ∆ABC as given and construct ∠XBC of the required measure at B as shown.

2. From the ray, BX cut an arc equal to AB – AC at point P and join it to C as shown

3. Draw the perpendicular bisector of PC and let it intersect BX at point A as shown:

4. Join AC, ∆ABC is the required triangle.

Hence, it is clear that a perpendicular bisector is required in the process.

### Question 9

A triangle ABC has base angle 45∘. It's perimeter is [2+√2]. What type of triangle is it?

Isosceles triangle

Right triangle

Can't be determined

Scalene triangle

#### SOLUTION

Solution :C

The information given above is insufficient to construct a triangle. So, the triangle cannot be constructed and its characteristics can’t be determined.

### Question 10

The construction of ΔABC, given that BC = 12 cm, is possible when the difference of AB and AC equals

12.5 cm

8 cm

#### SOLUTION

Solution :B and C

The difference between two sides of a triangle should be smaller than the third side. So only 8 cm and 10 cm can be the possible difference.