Construction of Quadrilaterals

Venu wants to construct a quadrilateral $ABCD$, $AB=4 cm, BC=5 cm, CD=6.5 cm$ and $\angle B = 105°$ and $\angle C = 80°$.  She made a rough sketch with the given information. Which of the following can be her next step?

Write the steps for the construction of a trapezium $\mathrm{ABCD}$ in which $\mathrm{AB}\parallel \mathrm{CD}, \mathrm{AB}=8 \mathrm{cm}, \mathrm{BC}=6 \mathrm{cm}, \mathrm{CD}=4 \mathrm{cm}$ and $\angle \mathrm{B}={60}^{\mathrm{o}}$.

Construct a quadrilateral $\mathrm{PQRS}$, with the base angles of $100°$ each at $\mathrm{P}$ and $\mathrm{Q}$ and $\angle \mathrm{R}$ equals to $120°$.

Write the steps for the construction of a quadrilateral $\mathrm{L}\mathrm{I}\mathrm{F}\mathrm{T}$, with $\mathrm{L}\mathrm{I}=4 \mathrm{c}\mathrm{m}$, $\mathrm{IF}=3 \mathrm{cm}$ $\mathrm{T}\mathrm{L}=2.5 \mathrm{c}\mathrm{m}$, $\mathrm{L}\mathrm{F}=4.5 \mathrm{c}\mathrm{m}$ and $\mathrm{I}\mathrm{T}=4 \mathrm{c}\mathrm{m}$.

Construct a quadrilateral $PQRS$ in which $PQ=7 \mathrm{cm}, QR=6.5 \mathrm{cm}, RS=5.2 \mathrm{cm}, SP=4.40 \mathrm{cm}$ and $\angle PQR=60°$.

Arrange the steps of construction while constructing a quadrilateral $ABCD$ given $AB=5.3 \mathrm{cm}, AD=2.9 \mathrm{cm}, A=70°$, $\angle B=95°$ and $\angle C=85°$.

Step $1$: With $A$ as centre and radius $2.9 \mathrm{cm},$ draw an arc to cut $AX$ at $D$.

Step $2$: At $B$, draw $\angle ZBA=95°$ so that $ZB$ intersects $YD$ at $C$.

Step $3$: Draw $AB=5.3 \mathrm{cm}$.

Step $4$: At $D$, draw $\angle ADY=110°$.

Step $5$: At $A$, draw $\angle XAB=70°$.

A _____ cannot be constructed with the data of the three angles alone, the measurements of the two included sides are also required.

It is possible to construct a square $\mathrm{ABCD}$ having $\mathrm{AC}=6.8$ cm.

If a quadrilateral $\mathrm{ABCD}$ has  $AC=6.6$ cm and the diagonals intersecting at $60°$ then it is a rectangle.

 A diagonal of a quadrilateral is a line segment that joins two _____ vertices of the quadrilateral. (Opposite/Adjacent)

Which type of quadrilateral is obtained by measurements given below:

A quadrilateral $\mathrm{CART}$ with $\mathrm{CR}=6 \mathrm{cm}, \mathrm{AT}=4.8 \mathrm{cm}$

Can you draw a parallelogram $\mathrm{BATS}$ where $\mathrm{BA}=5 \mathrm{cm}$, $\mathrm{AT}=6 \mathrm{cm}$ and $\mathrm{AS}=6.5 \mathrm{cm}$? (Yes/No)

Suppose the two diagonals of a Rhombus are equal in length. Which quadrilateral do you obtain? 

Can you construct the below quadrilateral $\mathrm{ABCD}$ by taking $\mathrm{BC}$ as base instead of $\mathrm{AB}$? (Yes/No)

Can you construct the quadrilateral $\mathrm{PLAN}$ if $\mathrm{PL}=6 \mathrm{cm}$, $\mathrm{LA}=9.5 \mathrm{cm}$, $\angle \mathrm{P}=75°$ , $\angle \mathrm{L}=15°$ and $\angle \mathrm{A}=140°$ . (yes/no)

Can you construct the above quadrilateral $\mathrm{PQRS}$, if we have an angle of $100°$ at $\mathrm{P}$ instead of $75°$. [Yes / No]

Given a Quadrilateral $\mathrm{ABCD}$, given $\mathrm{AB}=5.4 \mathrm{cm}, \mathrm{BC}=3.8 \mathrm{cm}, \mathrm{DA}=3.8 \mathrm{cm}, \angle \mathrm{ABC}=80°, \angle \mathrm{DAB}=100°$. Name the quadrilateral that can be constructed.

A quadrilateral $\mathrm{ABCD}$ can be constructed with $\mathrm{AB}=6 \mathrm{cm}, \mathrm{BC}=7 \mathrm{cm}, \mathrm{CD}=3 \mathrm{cm}, \mathrm{AD}=5.5 \mathrm{cm}$ and $\mathrm{AC}=11 \mathrm{cm}$.

Construct a trapezium $PQRS$ with $PS\parallel QR$, $QR=8 \mathrm{cm}$, $PQ=$$4.1 \mathrm{cm}$ and $PS=5 \mathrm{cm}$ and $\angle Q=90°$.

Construct a trapezium ABCD with AB||DC, DC=6 cm, $\angle$D=${60}^0$, AD=$4$ cm and AB=$3.5$ cm.