Construction of Trapezium When Its Three Sides and One Diagonal Are Given

Q. Akash draws a straight line on a sheet of paper. Then he draws another line such that the distance between the two lines is same throughout. Similarly, he draws one more line in the same manner. He names these lines as l, m and n. Which of the following is correct? ( Select all that apply)

1. l $\parallel$ m
2. m $\parallel$ n
3. l $\parallel$ m $\parallel$ n
4. l$\text{/}$ $\parallel$m $\parallel$ n

Q.

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

1. $4$

2. $3$

3. $2$

4. $1$

Q. Show that the line segment which joins the midpoints of oblique sides of a trapezium is parallel to the parallel sides.

Q. Suppose you are given the lengths of 3 sides and one diagonal in a trapezium, how many unique trapeziums can you draw?

1. 1
2. 2
3. 3
4. Data insufficient for construction

Q.

If we know that one side of the rectangle is 8 cm, can we construct a unique rectangle?

1. Yes, we can

2. With measurement of one angle, yes

3. With measurement of two angles, yes

4. No, its not possible

Q. To construct a trapezium PQRS with $PQ\parallel RS,$ the following measurements are given:
PQ = 8 cm, QR = 9 cm and $\angle PQR={60}^{\circ }.$
Which other measure will help complete the construction?

1. PA, the altitude from the point P onto RS.
2. RB, the altitude from the point R onto PQ.
3. We need at least two more measures to uniquely construct this trapezium.
4. $\angle SPQ$

Q. To construct a trapezium ABCD with $AB\parallel CD,$ the following measurements are given:
AB = 5.5 cm, BC = 4.9 cm and CD = 5.9 cm.
Which other measure will help complete the construction?

1. AD
2. DB
3. Altitude AE of ABCD
4. $\angle ABC$

Q.

The number of parameters required to construct a quadrilateral is ___. Choose the most appropriate answer to fill in the blank.

1. 5

2. 2

3. 4

4. 3

Q. The $1^{st}$ step is?

1. Draw an arc of length $CD$ on the line $\parallel AB$. Join $C-D$
2. Draw a line from $C\parallel AB$
3. Draw an arc of length $BC$ from $B$ and of length $AC$ from $A$ and mark the intersection point as $C$. Join $B-C$ and $A-C$
4. Draw base $AB$

Q. The $4^{th}$ step is:

1. Draw an arc of length $CD$ on the line $\parallel AB$. Join $C-D$
2. Draw base $AB$
3. Draw a line from $C\parallel AB$
4. Draw an arc of length $BC$ from $B$ and of length $AC$ from $A$ and mark the intersection point as $C$. Join $B-C$ and $A-C$

Q. In trapezium PQRS, side $PQ||RS$ and $PQ=3cm,RS=7cm$ the distance between them is $4cm$ find its area .

Q.

Which of the following measurements of trapeziums PQRS with PQ||RS are suitable for its construction?

1. PQ = 8 cm, QR = 3 cm, RS = 5 cm, ∠P = 50^o and ∠S = 130^o

2. PQ = 9 cm, QR = 7 cm, RS = 5.5 cm, ∠P = 80^o and ∠S = 110^o

3. PQ = 6 cm, QR = 4 cm, RS = 2 cm, ∠Q = 65^o and ∠R = 115^o

4. PQ = 7.5 cm, QR = 5 cm, RS = 4 cm, ∠Q = 40^o and R = 120^o

Q.

Which of the following measurements of trapeziums PQRS with PQ||RS are suitable for its construction?

1. 

2. 

3. 

4. 

Q. To construct a trapezium ABCD with $AB\parallel CD,$ the following measurements are given:
AB = 5.5 cm, BC = 4.9 cm and CD = 5.9 cm.
Which other measure will not help complete the construction?

1. $\angle ABC$
2. AD
3. DB
4. Altitude AE of ABCD

Q. For constructing a unique quadrilateral when 2 sides and 3 angles are given, the length of sides are mandatory.

1. two opposite
2. two adjacent
3. any two

Q. The $3^{rd}$ step is:

1. Draw an arc of length $CD$ on the line $\parallel AB$. Join $C-D$
2. Draw a line from $C\parallel AB$
3. Draw an arc of length $BC$ from $B$ and of length $AC$ from $A$ and mark the intersection point as $C$. Join $B-C$ and $A-C$
4. Draw base $AB$

Q. The $2^{nd}$ step is:

1. Draw an arc of length $CD$ on the line $\parallel AB$. Join $C-D$
2. Draw an arc of length $BC$ from $B$ and of length $AC$ from $A$ and mark the intersection point as $C$. Join $B-C$ and $A-C$
3. Draw a line from $C\parallel AB$
4. Draw base $AB$