Construction of Special Type of Quadrilaterals

A rhombus can be constructed if the measure of one side and _____ or _____ is known.

Necessary conditions for the construction of unique parallelogram are

Necessary conditions for the construction of unique rhombus are

Construct the below-given rhombus by taking $\mathrm{BD}$ as a base instead of $\mathrm{AC}$.

Write the steps for constructing a unique rectangle $PQRS$, if you know only the lengths $PQ$and $QR$?

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 $C$.

Construct a square whose diagonal is $7 cm$. 

Construct a square whose diagonal is $6.8 cm$. 

Construct a rectangle $PQRS$ whose diagonal $PR=6cm$ and the angle between the diagonal is $40°$.

Construct a rectangle whose one diagonal has length $5 cm$ and the angle between the diagonals is $50°$

Construct a rectangle $ABCD$. Diagonal $AC=8cm$ and angles between the diagonals$=45°$

Write the necessary condition to construct a rectangle.

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 $7.2 \mathrm{cm}$.

A quadrilateral $PQRS$ in which $QS=6 \mathrm{cm}$ and $PR=8 \mathrm{cm}$ are perpendicular to each other, is a _____. (Kite/Rhombus/Parallelogram)

It is possible to construct a Rectangle with one side is of $3 \mathrm{cm}$ whose diagonal is $4.5 \mathrm{cm}$.

A quadrilateral $\mathrm{ABCD}$ in which $\mathrm{AC}=6$ cm and  $\mathrm{BD}=4$cm are perpendicular to each other is a _____ . (Square/Rhombus/Parallelogram)

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.

Can you construct the below quadrilateral (rhombus) by taking $\mathrm{BD}$ as a base instead of $\mathrm{AC}$ ? (Yes/No)

Construct the following squares with the given measurements and also find their area.

$REST, ET=8 \mathrm{cm}$

Construct the following rectangles with the given measurements and also find their area.

$BAND\mathit{,}\mathit{ }BA=7.2 \mathrm{cm}$ and $BN=9.7 \mathrm{cm}$.