Answer: Option B. -> AC
:
B
Minimum number of measures required to construct a rhombus are 2.
If one side of a rhombus is specified, another measurementthat must be specified to construct a rhombus is its diagonal or one of the angles.
Thus, the correct answer is AC as it is diagonal.

Answer: Option A. -> Rhombus
:
A

If I combine2 equilateral triangles, I get a quadrilateral with all sides equal. Since the angle of an equilateral triangle is ${60}^{\circ }$, no sides will be perpendicular. The quadrilateral formed cannot be a square. Hence, it is a rhombus.

Answer: Option D. -> With the measure of BC, Yes
:
D
We can't draw a unique quadrilateral with all the measurements which are given. This is because we need the measurement of two adjacent sides and 3 angles to construct the quadrilateral ABCD.But with BC, we will have 6 sets of measurements and two known adjacent sides. Hence, we will be able to construct the quadrilateral ABCD.

Answer: Option B. -> False
:
B
Any four measurements are not sufficient to draw a unique quadrilateral.
Let us take AB = 5cm, BC = 4cm, AD = 5cm, CD = 3cm.
We shall start constructing with any one side (say AB). Construct AB with length 5cm. Now, as we have BC and AD. We can draw arcs with BC and AD as radii. But we cannot mark the points C and D based on the data given. So, we need more data to draw a quadrilateral.

Answer: Option A. -> Draw line segment
:
A
Suppose, we have to draw a quadrilateral. The length of three given sides are 'a' units, 'b' units and 'c' units. The measure of two given angles is $\alpha$ and $\beta$.
The first step is to construct a line segment AB = 'a' units. Taking AB as the base, we construct a line making an angle $\alpha$ with the line segment AB. We cut the line by an arc of length 'b' units taking B as center and mark point where arc cuts the line as C.
Taking BC as the base, we construct a line making an angle $\beta$ with the line segment BC.We cut the line by an arc of length 'c' units taking C as center and mark point where arc cuts the line as D.
The final step is to join A and D to complete the quadrilateral ABCD.

Answer: Option A. -> Yes
:
A
Let us try to draw the quadrilateral:
Step 1: Draw BC = 6 cm.
Step 2: At B, draw an angle = ${60}^{\circ }$. Along that angle, make an arc of 5 cm and mark it as pointA.
Step 3: From A, draw an arc of 6 cm.
Step 4: From C, draw an arc of 7 cm such that it intersects the arc made from A. Mark the point of intersection as D.
Step 5: Join ABCD to complete the quadrilateral.
Is this quadrilateral unique? Yes it is.
If we move it, keeping all the angle length constant $△$ ABC will change. So, there is only one quadrilateral ABCD with AB = 5 cm, BC = 6 cm, CD = 7 cm, BA = 6 cm, $\angle$ABC= ${60}^{\circ }$.

:
Since all the sides of a rhombus are equal, it means that if we know one side we know all the sides.
Now, while constructing the rhombuswe need to know at least one angle (as all the angles in a rhombus are not equal). Therefore, in total we need at least 2 measurements to construct a unique rhombus.

Answer: Option A. -> No, it is impossible
:
A
If we have the measures of all the sides of a quadrilateral and its one diagonal, we can draw two triangles and hence, form a quadrilateral.
ABCD comprises of two triangle$△$ADB &$△$CDB
InΔ ADB, AB = 3cm, BD = 8cm, and AD = 4cm
Since, AB + AD $<$BD
$△$ADB can't be constructed.
So, quadrilateral ABCD can't be constructed.

Answer: Option D. -> No, its not possible
:
D
Rectangle is a special quadrilateral and minimum number of measures required to construct a rectangle is 2(length of 2 sides).
Sincewe only know one side of the rectangle. we can draw infinite rectangles. This is because the other side's length is not specified. For e.g.

Answer: Option A. -> Yes, it is possible
:
A
Step 1: Draw AB = 5cm.
Step 2: At B, draw an angle of ${45}^{\circ }$ and mark 6 cm along that angle. Mark the point as C.
Step 3: At C, draw an angle of ${55}^{\circ }$ and mark 7cm along that angle. Mark the point as D.
Step 4: Join point A and D. So, quadrilateral ABCD can be constructed.