Practical Geometry Test

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Practical Geometry Test - 1

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Question 1
1 / -0

To construct a unique parallelogram, the minimum number of measurements required is

A
2

B
3

C
4

D
5

Solution

Since, parallelogram is a quadrilateral with opposite sides are parallel and equal, we need at least 3 measurements to construct the same. These three measurements are the length of 2 adjacent sides and 1 angle (including).

The angle is required to construct two adjacent sides of given length. Then, adjacent angle can be drawn as both adjacent angles of a parallelogram are supplementary. The other 2 angles and 2 sides can be drawn by these measurements as opposite sides and opposite angles of a parallelogram are equal.
Question 2
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Arrange the following steps of construction in the correct order while constructing a rectangle PQRS, given PR = 5.8 cm and angle between the diagonals equal to 60°.

1. From O, draw arcs of radius equal to 2.9 cm to intersect OA at S and OB at D.
2. Draw the perpendicular bisector of PR and find the mid-point of PR. Let the perpendicular bisectors intersect at O.
3. Join PS, RS, PQ and QR.
4. Through O, construct a line AOB such that ∠AOR = 60°.
5. Draw a line segment PR = 5.8 cm.

Then, PQRS is the required rectangle

A
5, 2, 4, 1, 3

B
3, 2, 5, 4, 1

C
2, 4, 5, 1, 3

D
1, 5, 3, 2, 4

Solution

5. Draw a line segment PR = 5.8 cm.
2. Draw the perpendicular bisector of PR and find the mid-point of PR.
Let the perpendicular bisectors intersect at O.
4. Through O, construct a line AOB such that ∠AOR = 60°.
1. From O, draw arcs of radius equal to 2.9 cm to intersect OA at S and OB at Q.
3. Join PS, RS, PQ and QR.

PQRS is the required rectangle.
Question 3
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Which of the following is necessary to draw a parallelogram?

A
Two unequal lines and two equal lines

B
Two pairs of straight lines

C
Four 90° angles

D
Two pairs of parallel lines

Solution

Two pairs of parallel lines are necessary to draw a parallelogram.
Question 4
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Which of the following statements is true about a triangle PQR, where PQ = 7 cm, QR = 5 cm and RP = 15?

A
It is possible to make a triangle from these conditions.

B
It is not possible to make a triangle from these conditions.

C
Angle PQR = 90°

D
None of these

Solution

The triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
But according to the given conditions in question, PQ + QR < RP
So, it is not possible to make a triangle using the given condition.
Question 5
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Which of the following parts is/are necessary to construct a quadrilateral PQRS?

A
Length of QR

B
Length of PQ

C
Measures of angles P, Q and R

D
All of the above

Solution

To construct a quadrilateral PQRS, measure of at least 5 parts are necessary.
When four sides and one diagonal are given.

When two diagonals and three sides are given.
When two adjacent sides and three angles are given.

When three sides and two included angles are given.

So, for quadrilateral PQRS, lengths of PQ, QR and measures of angles P, Q and R are required.
Question 6
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Which of the following properties of a rhombus will not be helpful in its construction?

A
Adjacent sides of a rhombus

B
Diagonals of a rhombus

C
Adjacent angles of a rhombus

D
Both (1) and (3)

Solution

Rhombus is a quadrilateral in which all sides are equal and opposite sides are parallel. Moreover, its diagonals bisect each other at 90°. So, in order to construct a rhombus we need at least one of the following measurements.

(1) Adjacent sides and one angle (including).
(2) Both the diagonals of rhombus.
(3) Adjacent angles and one side of rhombus.
Question 7
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Arrange the steps of construction while constructing a quadrilateral given MO = 6 cm, OR = 4.5 cm,
∠M = 60° ∠O = 105° ∠R = 105°

Step 1: Also construct an angle 105° at R and produce the side RE.
Step 2: Construct another angle of 60° at point M and produce the side ME. Both sides ME and RE intersect at E.
Step 3: It is the required quadrilateral.
Step 4: Draw a line segment MO = 6 cm.
Step 5: Construct ∠O = 105° and taking radius 4.5 cm, draw an arc taking O as centre, which intersects at R.

A
4, 5, 1, 2, 3

B
1, 5, 4, 2, 3

C
4, 1, 5, 2, 3

D
4, 5, 1, 3, 2

Solution

Arranging these steps the answer becomes

1. Draw a line segment MO = 6 cm.
2. Construct ∠O = 105° and taking radius 4.5 cm, draw an arc taking O as centre, which intersects at R.
3. Also construct an angle 105° at R and produce the side RE.
4. Construct another angle of 60° at point M and produce the side ME. Both sides ME and RE intersect at E.
5. It is the required quadrilateral.

Question 8

1 / -0

Match the following:

Column I	Column II
1. Construction of a unique parallelogram can be possible if atleast	(A) three sides and one angle are given.
2. Construction of a rhombus can be possible if only	(B) two sides are given.
3. Construction of an isosceles trapezium can be possible if only	(C) two sides and one angle is given.
4. Construction of a rectangle can be possible if only	(D) one angle and one side is given.

1 - (C), 2 - (D), 3 - (B), 4 - (A)

1 - (B), 2 - (D), 3 - (A), 4 - (C)

1 - (C), 2 - (D), 3 - (A), 4 - (B)

1 - (B), 2 - (A), 3 - (D), 4 - (C)

Solution

Column I	Column II
1. Construction of a unique parallelogram can be possible if atleast	(C) two sides and one angle is given.
2. Construction of a rhombus can be possible if only	(D) one angle and one side is given.
3. Construction of an isosceles trapezium can be possible if only	(A) three sides and one angle are given.
4. Construction of a rectangle can be possible if only	(B) two sides are given.

Question 9
1 / -0

Which of the following cases is incorrect in terms of construction of a kite?

A
Two unequal sides and one diagonal is given (excluded).

B
Two unequal sides and one diagonal is given (included).

C
Two adjacent sides and one angle (included) is given.

D
Two diagonals and one side is given.

Solution

This is incorrect because: A kite cannot be constructed with the two adjacent sides and one angle (included). We need atleast one of the diagonals with the given information.

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Practical Geometry Test - 1

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Practical Geometry Test - 1

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Question 1

2

3

4

5

Solution

Question 2

5, 2, 4, 1, 3

3, 2, 5, 4, 1

2, 4, 5, 1, 3

1, 5, 3, 2, 4

Solution

Question 3

Two unequal lines and two equal lines

Two pairs of straight lines

Four 90° angles

Two pairs of parallel lines

Solution

Question 4

It is possible to make a triangle from these conditions.

It is not possible to make a triangle from these conditions.

Angle PQR = 90°

None of these

Solution

Question 5

Length of QR

Length of PQ

Measures of angles P, Q and R

All of the above

Solution

Question 6

Adjacent sides of a rhombus

Diagonals of a rhombus

Adjacent angles of a rhombus

Both (1) and (3)

Solution

Question 7

4, 5, 1, 2, 3

1, 5, 4, 2, 3

4, 1, 5, 2, 3

4, 5, 1, 3, 2

Solution

Question 8

1 - (C), 2 - (D), 3 - (B), 4 - (A)

1 - (B), 2 - (D), 3 - (A), 4 - (C)

1 - (C), 2 - (D), 3 - (A), 4 - (B)

1 - (B), 2 - (A), 3 - (D), 4 - (C)

Solution

Question 9

Two unequal sides and one diagonal is given (excluded).

Two unequal sides and one diagonal is given (included).

Two adjacent sides and one angle (included) is given.

Two diagonals and one side is given.

Solution

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