# Free Practical Geometry 03 Practice Test - 8th Grade

There is a quadrilateral PLAY with PL = 3cm,  LA = 4cm, AY = 4.5 cm, PY = 2cm. Which of the following values of LY is not possible?

A.

2

B.

3

C.

6

D.

4

#### SOLUTION

Solution : C

Since one side of a triangle cannot be greater than the sum of the other two sides, diagonal LY must be smaller than the sum of PL + PY and smaller than the sum of AL + AY. PL + PY =5 and AL + AY = 8.5. Hence, LY must be less than 5. Thus, the correct answer is 6. A rhombus ABCD is to be constructed with side AB = 5 cm. Which of the following dimensions must also be specified to construct the rhombus?

A.

AD

B.

AC

C.

BC

D.

None of these

#### SOLUTION

Solution : B

Minimum number of measures required to construct a rhombus are 2.
If one side of a rhombus is specified, another measurement that must be specified to construct a rhombus is its diagonal or one of the angles.
Thus, the correct answer is AC as it is diagonal.

To construct a parallelogram, a minimum of how many measurements need to be provided?

A.

1

B.

2

C.

3

D.

4

#### SOLUTION

Solution : C

To construct a parallelogram both unequal sides need to be provided. Other than this one angle or one diagonal should be provided. Hence, a minimum of 3 measurements are needed. With which of the following given measurements, a unique Kite named EASY can be formed?

A.

EA = 5 cm, AS = 7 cm and EAS = 115

B.

EA = 7 cm, AS = 12 cm and ES = 22 cm

C.

AS = 3 cm, EY = 7 cm

D.

ES = 15 cm and EAS = 120

#### SOLUTION

Solution : A and B

A Kite is a quadrilateral in which both the adjacent sides are equal to each other. Also, one of the opposite angles is equal. Therefore, to construct a Kite, length of two unequal sides must be given. Also, the length of the diagonal or the measure of any one of the angles must be given.

What is drawn in the first step in constructing a quadrilateral for which 2 sides and 3 angles are known?

A.

Arc

B.

Line Segment

C.

Triangle

D.

None of these

#### SOLUTION

Solution : B

Drawing a line segment, which lies in between two given angles, is the first step in this construction. After the line segment is constructed, angles are drawn using that line segment as the base.

Suppose you are asked to construct a square having side length 'a' units. This information is enough to construct a square.

A.

True

B.

False

#### SOLUTION

Solution : A

As all the sides are equal and all the angles measure 90 degrees in a square, the given information is enough to construct a square.

What is the last step in constructing quadrilateral with 3 sides and 2 included angles given?

A.

Draw line segment

B.

Draw arc

C.

Construct triangle

D.

None of these

#### SOLUTION

Solution : A

Suppose, we have to draw a quadrilateral. The length of three given sides are 'a' units, 'b' units and 'c' units. The measure of two given angles is α and β
The first step is to construct a line segment AB = 'a' units. Taking AB as the base, we construct a line making an angle α with the line segment AB. We cut the line by an arc of length 'b' units taking B as center and mark point where arc cuts the line as C.
Taking BC as the base, we construct a line making an angle β with the line segment BC. We cut the line by an arc of length 'c' units taking C as center and mark point where arc cuts the line as D.
The final step is to join A and D to complete the quadrilateral ABCD.

When we start constructing a quadrilateral whose 2 diagonals and 3 sides known, in how many ways can the construction be started.

A.

1

B.

2

C.

3

D.

4

#### SOLUTION

Solution : B

To construct a quadrilateral, we need to construct two triangles. As, both the diagonals are known, we can construct any of the two triangles first. Thus, there are two ways to start this construction.

Which of the following geometric apparatus is used to make two line segments meet when their lengths and one point in each line segment is known?

A.

Compass

B.

Protractor

C.

Divider

D.

Set Square

#### SOLUTION

Solution : A

To make the two line segments meet, arcs are drawn and their intersection point is found. A compass is hence used.

While constructing quadrilateral PQRS with 3 sides and 2 diagonals which of the following geometric tool is not used?

A.

Ruler

B.

Protractor

C.

Compass

D.

Divider

#### SOLUTION

Solution : B

3 sides and 2 diagonals of a quadrilateral is known. This information is enough to construct a quadrilateral. Thus, a protractor is not necessary for the construction because no angles are measured or drawn during construction.