Practical Geometry Test

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Practical Geometry Test - 4

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Question 1
1 / -0

Given below are the steps for construction of a quadrilateral ABCD, where AC = 5.5 cm, BD = 7 cm, BC = 4.5 cm, AD = 5.5 cm and CD = 5 cm. Which of the following steps is incorrect?

Step (1): Draw AC = 5.5 cm.
Step (2): With A as the centre and radius 5.5 cm, draw an arc.
Step (3): With C as the centre and radius 5 cm draw another arc, cutting the previous arc at D. Join AD and DC.
Step (4): With D as the centre, draw an arc of radius 7 cm on the opposite side of AC.
Step (5): With C as the centre, draw an arc of 5 cm cutting the arc drawn in above step at B.
Step (6): Join AB, BC and BD.

A
Step 2

B
Step 3

C
Step 4

D
Step 5

Solution

Step 5 is incorrect as with C as the centre, we need to draw an arc of 4.5 cm cutting the arc drawn in step 4 at B, as BC = 4.5 cm.
The figure below is not drawn to scale.
Question 2
1 / -0

Draw a parallelogram MATH, where MA = 5.6 cm and AT = 4.8 cm. Is the given information sufficient for that?

A
Yes, as the two non-parallel sides are given.

B
No, because no angle is provided.

C
No, because the diagonals are not given.

D
Either (2) or (3)

Solution

The given information is not sufficient to draw parallelogram MATH, where MA = 5.6 cm and AT = 4.8 cm.
We need at least one angle or the two diagonals to construct the parallelogram.
Question 3
1 / -0

Arrange the steps for the construction of a quadrilateral ACBD, where AB = 4.5 cm, BC = 5 cm, CA = 6 cm, DA = 5.5 cm and DB = 7.5 cm.

(1) Join DA and DB.
(2) Draw an arc of radius 5.5 cm taking A as the centre. Then, draw another arc of radius 7.5 cm taking B as the centre. Both arcs intersect at D.
(3) Draw AB = 4.5 cm.
(4) Join CA and BC.
(5) Draw arcs of radii 6 cm and 5 cm taking A and B, respectively, as centres, at opposite sides which intersect at C.

A
(1), (2), (3), (4), (5)

B
(2), (3), (4), (5), (1)

C
(3), (2), (1), (5), (4)

D
(1), (2), (4), (3), (5)

Solution

Correct order of steps:

i) Draw AB = 4.5 cm

ii) Draw an arc of radius 5.5 cm taking A as the centre. Then, draw another arc of radius 7.5 cm taking B as the centre. Both arcs intersect at D.
iii) and iv)
Therefore, the correct order is:
(3) Draw AB = 4.5 cm.
(2) Draw an arc of radius 5.5 cm taking A as the centre. Then, draw another arc of radius 7.5 cm taking B as the centre. Both arcs intersect at D.
(1) Join DA and DB.
(5) Draw arcs of radii 6 cm and 5 cm taking A and B, respectively, as centres, at opposite sides which intersect at C.
(4) Join CA and BC.

Note: All the above diagrams are not drawn to scale.
Question 4
1 / -0

Arrange the steps for construction of a parallelogram ABCD, where AB = 6 cm, BC = 7 cm and angle B = 85.(1) Join AD and CD.
(2) Cut an arc of radius 7 cm from point B and let this point be C.
(3) Draw an arc of radius 7 cm taking A as the centre. Draw another arc of radius 6 cm taking C as the centre.
(4) Draw an angle at B = 85°.
(5) Draw a line segment AB = 6 cm.

A
(5), (2), (4), (3), (1)

B
(5), (4), (1), (2), (3)

C
(5), (4), (3), (2), (1)

D
(5), (4), (2), (3), (1)

Solution

(5) Draw a line segment AB = 6 cm.
(4) Draw an angle at B = 85°.
(2) Cut an arc of radius 7 cm from point B and let this point be C.
(3) Draw an arc of radius 7 cm taking A as the centre. Draw another arc of radius 6 cm taking C as the centre.
(1) Join AD and CD.
Question 5
1 / -0

Which of the following quadrilaterals can be formed using the information given below:

Diagonals AC = 5.4 cm and BD = 6.2 cm bisect each other and one of the angles between them is 70°.

A
Square

B
Rectangle

C
Parallelogram

D
Rhombus

Solution

i) Angle between the diagonals of a square is 90°, and can never be 70°.
ii) Diagonals of a rectangle are equal.
iii) Only a parallelogram can be formed as the diagonals of a parallelogram are not equal, and they bisect each other.
iv) Diagonals of a rhombus are perpendicular bisectors and the angle between them cannot be 70°.
So, option (3) is correct.
Question 6
1 / -0

Given below are the steps for construction of a quadrilateral ABCD, where AB = 4.6 cm, ∠ABC = 80°, BC = 5 cm, ∠BAD = 120° and AD = 6 cm. Which of the following steps is/are INCORRECT?

Step 1: Draw AB = 4.6 cm.
Step 2: Make ∠ABX = 80°.
Step 3: With B as the centre and radius equal to 6 cm, draw an arc cutting BX at C.
Step 4: Make ∠BAY = 120°.
Step 5: With A as the centre and 5 cm as radius, draw an arc cutting AY at D.
Step 6: Join CD.

A
Step 4

B
Step 3

C
Step 3 and Step 5

D
Step 2 and Step 3

Solution

Step 3: With B as the centre and radius equal to 6 cm, draw an arc cutting BX at C.
This is incorrect. Instead, with B as the centre and radius equal to 5 cm, we should draw an arc cutting BX at C.
Step 5: With A as the centre and 5 cm as radius, draw an arc cutting AY at D.
This is incorrect. Instead, with A as the centre and 6 cm as radius, draw an arc cutting AY at D.
Question 7
1 / -0

To construct a trapezium, which of the following pieces of information is sufficient?

A
Two parallel sides with one non-parallel side and two diagonals

B
Two parallel sides and one angle

C
Two diagonals and one angle

D
None of the above

Solution

If two parallel sides with one non-parallel side and two diagonals are given, we can construct a trapezium.
Question 8
1 / -0

Which of the following statements is/are true for the construction of a kite ABCD, where AB = 5 cm, BC = 6 cm, CD = 5 cm and BD = 7 cm?

(A) It is possible to draw the kite.
(B) It is not possible to draw the kite because AB = CD.
(C) It is not possible as BC ≠ AD.
(D) It is not possible to draw the kite because AB ≠ BC and AD ≠ CD.

A
Only (D)

B
Only (B) and (D)

C
Only (B) and (C)

D
Only (A)

Solution

In case of a kite, we know that adjacent sides are equal and opposite sides are unequal.
Using the above property, we can say that we can't draw a kite using the given data.
It is given that:
i) AB = CD
ii) AB ≠ BC and AD ≠ CD
So, both statements (B) and (D) are correct.
Question 9
1 / -0

To construct a quadrilateral JUMP, which of the following pieces of information is necessary?

A
Lengths of JU and JP

B
Lengths of UM, MP and UP

C
Both (1) and (2)

D
None of these

Solution

To construct a quadrilateral, the lengths of the four sides and one of the diagonals should be known.
So, both (1) and (2) are necessary.
Question 10
1 / -0

What information about a square is necessary in order to construct it?

A
Length of one side

B
Length of one diagonal

C
Measure of each angle

D
Either (1) or (2)

Solution

All the angles of a square are 90°.
All sides of a square are equal. So, with the help of one side's length, we can construct the square.
If we have the diagonal's length, we can calculate the side of the square and easily construct the square.
Question 11
1 / -0

Arrange the steps for construction of a rectangle ABCD, where AB = 7 cm and BC = 8 cm.

(1) Draw angle ZAB = 90° and angle YBA = 90°.(2) Draw an arc of radius 8 cm taking A as the centre and mark it as D. Draw another arc of radius 8 cm taking B as the centre and mark it as C.
(3) Join C and D.
(4) Draw a line segment AB = 7 cm.

A
(4), (2), (1), (3)

B
(4), (1), (2), (3)

C
(4), (1), (3), (2)

D
(1), (2), (3), (4)

Solution

The steps for construction are as follows:
(4) Draw a line segment AB = 7 cm.
(1) Draw angle ZAB = 90° and angle YBA = 90°. Extend A to Z and B to Y.
(2) Draw an arc of radius 8 cm taking A as the centre and mark it as D. Draw another arc of radius 8 cm taking B as the centre and mark it as C.
(3) Join C and D.

Question 12

1 / -0

Match the following:

Column - I	Column - II
1. A rectangle can be drawn	A. if two adjacent sides and included angle is given
2. An isosceles triangle can be drawn if	B. opposite parallel sides and base angles are given
3. A parallelogram can be constructed	C. if two sides are given
4. A trapezium can be drawn if	D. two equal sides and included angle is given

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

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

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

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

Solution

(1) Let the unequal sides of the rectangles be 7 cm and 8 cm.

(2) An isosceles triangle can be drawn if two equal sides and included angle are given.

(3) Since opposite sides and opposite angles of a parallelogram are equal, we require two adjacent sides and only one included angle (as remaining angles will be known).

(4) A trapezium can be constructed if the opposite parallel sides and adjacent base angles are given.

Question 13
1 / -0

Arrange steps (a) to (d) in correct order in relation to the construction of a parallelogram LMNO, where LM = 8 cm, MN = 5 cm and diagonal LN = 6 cm.

First, draw LM = 8 cm.

(a) With L as the centre, draw an arc of radius 6 cm to cut the arc drawn in previous step.
(b) Join NO and LO.
(c) With N and L as centres, draw arcs of radii 8 cm and 5 cm, respectively, which cut each other at O.
(d) With M as the centre, draw an arc of radius 5 cm.

A
c - a - d - b

B
d - a - c - b

C
d - a - b - c

D
a - d - b - c

Solution

(d) With M as the centre, draw an arc of radius 5 cm.

(a) With L as the centre, draw an arc of radius 6 cm to cut the arc drawn in previous step.

(c) With N and L as centres, draw arcs of radii 8 cm and 5 cm, respectively, which cut each other at O.

(b) Join NO and LO.
Question 14
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In which of the following cases can a convex quadrilateral be constructed?

(a) If two diagonals and three sides are given
(b) If three sides and one included angle are given
(c) If four sides and one diagonal are given
(d) If two adjacent sides and two angles are given

A
Only 'a' and 'c'

B
Only 'c'

C
Only 'a', 'b' and 'c'

D
Only 'a', 'c' and 'd'

Solution

Five measurements can determine a quadrilateral uniquely.
Possibilities:
1) A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal are given.
2) A quadrilateral can be constructed uniquely if the lengths of its two diagonals and three sides are known.
3) A quadrilateral can be constructed uniquely if the lengths of two adjacent sides and three angles are known.
4) A quadrilateral can be constructed uniquely if the lengths of its three sides and two included angles are given.
Question 15
1 / -0

Given below are the steps required for the construction of a rhombus when the lengths of two diagonals are given. Which of the following steps is/are incorrect in construction of a rhombus LMNO, where LN = 8 cm and MO = 6 cm?

Step 1: Draw a line segment LN of length 8 cm.
Step 2: Draw a perpendicular bisector of side LN by drawing arcs from L and N both above and below the side.
Step 3: Cut arcs of radius 3 cm from the point of intersection of perpendicular bisector and LN on either side of LN. Let these points be M and O.
Step 4: Join L and M, M and N, L and O, N and O, and M and O.
Step 5: LMNO is the required rhombus.

A
Step 2

B
Step 2 and Step 3

C
Step 3

D
None of these

Solution

Step 1: Draw a line segment LN of length 8 cm.
Step 2: Draw a perpendicular bisector of side LN by drawing arcs from L and N both above and below the side.
Step 3: Cut arcs of radius 3 cm from the point of intersection of perpendicular bisector and LN on either side of LN. Let these points be M and O.
Step 4: Join L and M, M and N, L and O, N and O, and M and O.
Step 5: LMNO is the required rhombus.
None of the given steps is incorrect.

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Practical Geometry Test - 4

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Question 1

Step 2

Step 3

Step 4

Step 5

Solution

Question 2

Yes, as the two non-parallel sides are given.

No, because no angle is provided.

No, because the diagonals are not given.

Either (2) or (3)

Solution

Question 3

(1), (2), (3), (4), (5)

(2), (3), (4), (5), (1)

(3), (2), (1), (5), (4)

(1), (2), (4), (3), (5)

Solution

Question 4

(5), (2), (4), (3), (1)

(5), (4), (1), (2), (3)

(5), (4), (3), (2), (1)

(5), (4), (2), (3), (1)

Solution

Question 5

Square

Rectangle

Parallelogram

Rhombus

Solution

Question 6

Step 4

Step 3

Step 3 and Step 5

Step 2 and Step 3

Solution

Question 7

Two parallel sides with one non-parallel side and two diagonals

Two parallel sides and one angle

Two diagonals and one angle

None of the above

Solution

Question 8

Only (D)

Only (B) and (D)

Only (B) and (C)

Only (A)

Solution

Question 9

Lengths of JU and JP

Lengths of UM, MP and UP

Both (1) and (2)

None of these

Solution

Question 10

Length of one side

Length of one diagonal

Measure of each angle

Either (1) or (2)

Solution

Question 11

(4), (2), (1), (3)

(4), (1), (2), (3)

(4), (1), (3), (2)

(1), (2), (3), (4)

Solution

Question 12

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

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

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

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

Solution