Special Cases of Constructing a Quadrilateral

Necessary conditions for the construction of unique parallelogram are

Necessary conditions for the construction of unique Parallelogram are

Necessary conditions for the construction of unique rhombus are

What are the necessary conditions for the construction of unique rhombus?

Is it possible to construct a unique rectangle of length $7.9 \mathrm{cm}$. Justify your answer.

Construct a rectangle with side $6.3 \mathrm{cm}$ and a diagonal $9.3 \mathrm{cm}$.

Construct a rectangle of side $7 \mathrm{cm}$ and a diagonal $9 \mathrm{cm}$.

Construct a rhombus with side $5$ cm, and diagonal $6.8$ cm.

Construct a rhombus with the measure of diagonals is $5 \mathrm{cm}$ and $4 \mathrm{cm}$.

Construct a square with side $7.5 \mathrm{cm}$.

Construct a square of side $4.2 \mathrm{cm}$.

Construct a rhombus $ABCD$, in which length of the side $CD=6 \mathrm{cm}$ and diagonal $BD=8.5 \mathrm{cm}$.

Construct a rhombus $ABCD$, in which the length of the diagonals $AC=8 \mathrm{cm}$ and $BD=7 \mathrm{cm}$ are given.

Construct a rectangle $ABCD$, in which the lengths of sides $AB=4.8 \mathrm{cm}, and BC=6.2 \mathrm{cm}$.

Construct a parallelogram $\mathrm{PQRS}$ with the following details:
$\mathrm{PQ}=5.4 \mathrm{cm}$, $\mathrm{QR}=3.8 \mathrm{cm}$ and $\angle \mathrm{P}=75°$. 

Construct a rectangle $ABCD$, in which diagonal $\mathrm{BD}=6.5 \mathrm{cm}$ and the angle between the diagonals is $45°$

Arrange the steps of construction while constructing a parallelogram $ABCD$, given that $AB=5 \mathrm{cm}\mathit{,}BC\mathit{=}4\mathit{ }\mathrm{cm}$ and $\angle B=60°$.

$1$. With $A$ as a centre and radius equal to $4 \mathrm{cm}$, draw an arc cutting $AY$ at $D$.

$2$. At $A$, draw $\angle YAB=120°$. $[\because A+B=180°]$

$3$. At $B$, draw $\angle XBA=60°$.

$4$. Draw $AB=5 \mathrm{cm}.$

$5$. Join $\mathrm{CD}$.

$6$. With $B$ as centre and radius equal to $4 \mathrm{cm}$, draw an arc cutting $BX$ at $C$.

Identify the correct order of steps of construction of rhombus $ABCD$ whose side is $AB=7.2 \mathrm{cm}$ and one angle is $\angle A=60°$.

$1$. Draw a line $\mathrm{AD}$ of length $7.2 \mathrm{cm}$ at an angle of $60°$ with $AB$ using a protractor and a scale.

$2$. Now, from the points $\mathrm{D}$, draw an arc of radius $7.2 \mathrm{cm}$ which intersects the previous arc.

$3$. Draw a base of $7.2 \mathrm{cm}$.

$4$. From the points $\mathrm{B}$, draw an arc of radius $7.2 \mathrm{cm}$.

Which type of quadrilateral is formed by using following measurements:

A quadrilateral with $\mathrm{ABCD}$ having $\mathrm{AB}=5$ cm and $\mathrm{AC}=6$cm.

Which type of quadrilateral is obtained by following measurements?

Quadrilateral $\mathrm{ABCD}$ in which $\mathrm{AB}\parallel \mathrm{CD}, \mathrm{AB}=8 \mathrm{cm}, \mathrm{BC}=6 \mathrm{cm}, \mathrm{CD}=4 \mathrm{cm}$ and $\angle \mathrm{B}={60}^{\mathrm{o}}$.