Construction of Trapeziums

Q. Suppose you are given the lengths of all 4 sides and the sides which are parallel are specified, how many trapeziums can you draw?

1. 1
2. 2
3. 3
4. Data insufficient

Q. A quadrilateral with only one pair of opposite sides parallel is called a trapezium.

1. True
2. False

Q. How many unique trapeziums can be drawn given three sides and one angle?

1. 1
2. 2
3. 3
4. 4

Q. To construct a trapezium ABCD with $AB\parallel CD,$ AB = 8 cm, BC = 5 cm, AD = 6 cm and $\angle ABC={60}^{\circ },$ we follow the following steps:
1) Draw the line segment AB = 8 cm.
2) Construct the angle $\angle ABX={60}^{\circ }$ at B.
3) With B as centre, draw an arc of radius 5 cm cutting BX at C.

The next step is ___.

1. Draw CY parallel to AB.
2. Draw a line segment AY parallel to BC.
3. With A as centre, draw an arc of radius 6 cm cutting BX.
4. With B as centre, draw an arc of radius 6 cm cutting BX.

Q. To construct a trapezium ABCD with $AB\parallel CD,$ AB = 6.5 cm, BC = 6.2 cm, $\angle ABC={80}^{\circ }$ and $\angle DAB={105}^{\circ },$ we follow the following steps:
1) Draw the line segment AB = 6.5 cm.
2) Construct the angle $\angle ABX={80}^{\circ }$ at B.
3) With B as centre, draw an arc of radius 6.2 cm cutting BX at C.
4) Draw CD parallel to AB.
The next step involved in the construction is __.

1. From the point A, draw an arc of radius 6.2 cm cutting CY.
2. Construct the angle $\angle BAZ={105}^{\circ }$ at A cutting CY at D.
3. From the point A, draw an arc of radius 6.6 cm cutting CY.
4. Construct the angle $\angle BAZ={75}^{\circ }$ at A cutting CY at D.

Q. Which of the following properties are used in the construction of a trapezium when all four sides are given?

1. One pair of opposite sides are parallel
2. Adjacent angles are supplementary.
3. The two non-parallel sides are unequal.
4. The diagonals do not bisect each other.

Q. To construct a trapezium ABCD with $AB\parallel CD,$ the following measurements are given:
AB = 5.5 cm, BC = 4.9 cm and $\angle ABC={70}^{\circ }.$
Which other measure will help complete the construction?

1. $\angle DAB$
2. AE, the altitude from the point A onto CD.
3. CM, the altitude from the point C onto AB.
4. We need at least two more measures to uniquely construct this trapezium.