Practical Geometry Test

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Practical Geometry Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following steps is incorrect for constructing a quadrilateral ABCD in which AB = 5.1 cm, BC = 4.6 cm, CD = 3.9 cm, AD = 4.0 cm and diagonal AC = 6 cm?

Step 1: Draw AB = 5.1 cm. With A as centre and radius equal to 6 cm, draw an arc.
Step 2: With B as centre and radius equal to 4.6 cm, draw another arc, cutting the previous arc at C and join BC.
Step 3: With A as centre and radius equal to 4.0 cm, draw an arc.
Step 4: With C as centre and radius equal to 3.8 cm, draw another arc, cutting the previous arc at D.Join AD and CD.

Then, ABCD is the required quadrilateral.

A
Step 1 only

B
Step 2 only

C
Step 3 only

D
Step 4 only

Solution

With C as centre and radius equal to 3.9 cm, draw another arc, cutting the previous arc at D. Join AD and CD.
Then, ABCD is the required quadrilateral.With C as centre and radius equal to 3.9 cm, draw another arc, cutting the previous arc at D. Join AD and CD.
Then, ABCD is the required quadrilateral.
Question 2
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 3
1 / -0

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 4
1 / -0

Arrange the following steps of construction in the correct order while constructing a rhombus of side 3.2 cm with one of its angles equal to 65°.

Steps of Construction:

(1) Join PS.
(2) Construct ∠RQX = 115° and ∠QRY = 65°.
(3) Draw QR = 3.2 cm.
(4) Draw QP = 3.2 cm along QX and RS = 3.2 cm along RY.

A
2, 1, 4, 3

B
3, 2, 1, 4

C
3, 2, 4, 1

D
4, 2, 3, 1

Solution

Clearly, adjacent angle = (180° - 65°) = 115°
So, we may proceed according to the steps with order: 3, 2, 4, 1.
Question 5
1 / -0

If LM || NO, MN || LO and MN ⊥ ON in a quadrilateral LMNO in which side MN = 4 cm and diagonal MO = 6 cm, then which of the following figures can be constructed?

A
Rhombus

B
Rectangle

C
Square

D
Trapezium

Solution

LM || NO and MN || LO in quadrilateral LMNO in which side MN = 4 cm and diagonal MO = 6 cm.

That is, LM ⊥ MN and NO ⊥ LO.
So, MNO and MLO are right-angled triangles.

Using Pythagorean theorem, NO = LM = cm and MN = LO = 4 cm.

So, the quadrilateral is a rectangle. Hence, from the given information, only rectangle can be constructed.
Question 6
1 / -0

Given below are the steps of construction of a rhombus ABCD with side 9 cm and a diagonal 12 cm. Which of the following is an INCORRECT step?

Steps of Construction:
Step 1. Draw 12 cm.
Step 2. With A as centre and 9 cm as radius, draw two arcs on either side of AC.
Step 3. With C as centre and the same radius, draw two arcs on either side of AC to cut the arcs of step 2 at B and D, respectively.
Step 4. Join BD, AB and CD.

A
Step 4

B
Step 1

C
Step 3

D
Step 2

Solution

Step 4 is incorrect. And the correct step is: Join BD, AB, CD, BC and AD.
Question 7
1 / -0

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 8
1 / -0

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 9
1 / -0

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 10
1 / -0

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.
Hence, option 4 is correct.
Question 11
1 / -0

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 12

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 13
1 / -0

Arrange the steps of construction while constructing a quadrilateral.

Step 1: Draw a line segment PL = 4 cm.
Step 2: It is the required quadrilateral .
Step 3: Construct A = 110° at A and produce the side AN which intersects PN at N.
Step 4: Construct angle of 75° at L and with L as centre, draw an arc of radius 6 cm, which intersects at A.
Step 5: Construct angle of 90° at P and produce the side PN.

A
1, 4, 5, 2, 3

B
1, 3, 4, 5, 2

C
1, 5, 4, 2, 3

D
1, 5, 4, 3, 2

Solution

Step 1: Draw a line segment PL = 4 cm.
Step 5: Construct angle of 90° at P and produce the side PN.
Step 4: Construct angle of 75° at L and with L as centre, draw an arc of radius 6 cm, which intersects at A.
Step 3: Construct A = 110° at A and produce the side AN which intersects PN at N.
Step 2: It is the required quadrilateral.
Question 14
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.
Hence, option 3 is correct.
Question 15
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Which of the following steps is/are incorrect while constructing a parallelogram, given HE = 5 cm, EA = 6 cm, R = 85°?

Step 1: Draw a line segment HE = 5 cm.
Step 2: Construct H = 95° and draw an arc of radius 6 cm with centre H, which intersects at R.
Step 3: Join RH.
Step 4: Join RA
Step 5: Draw R = E = 85° and draw an arc of radius 6 cm with E as centre which intersects at A.
Step 6: It is the required parallelogram.

A
Steps 4 and 5

B
Step 5 only

C
Step 4 only

D
Step 2 only

Solution

Both step 4 and 5 are incorrect because the correct order is

Step 1: Draw a line segment HE = 5 cm.
Step 2: Construct H = 95° and draw an arc of radius 6 cm with centre H, which intersects at R.
Step 3: Join RH.
Step 4: Draw R = E = 85° and draw an arc of radius 6 cm with E as centre which intersects at A.
Step 5: Join RA
Step 6: It is the required parallelogram