Constructing a Quadrilateral

Construct the following Quadrilateral $\mathrm{LIFT}$

$\mathrm{LI}=4 \mathrm{cm}, \mathrm{IF}=3 \mathrm{cm}, \mathrm{TL}=3 \mathrm{cm}, \mathrm{LF}=4.5 \mathrm{cm}, \mathrm{IT}=4 \mathrm{cm}$.

Construct the following Quadrilateral $\mathrm{PLAN}$

$\mathrm{PL}=4 \mathrm{cm}, \mathrm{LA}=6 \mathrm{cm}, \angle \mathrm{P}=90°, \angle \mathrm{A}=110°, \angle \mathrm{N}=85°$.

Construct the following Quadrilateral $\mathrm{MORE}$

$\mathrm{MO}=6 \mathrm{cm}, \mathrm{OR}=5 \mathrm{cm}, \angle \mathrm{M}=60°, \angle \mathrm{O}=105°, \angle \mathrm{R}=105°$.

Construct the following Quadrilateral $\mathrm{TRUE}$

$\mathrm{TR}=4 \mathrm{cm}, \mathrm{RU}=3 \mathrm{cm}, \mathrm{UE}=4 \mathrm{cm}, \angle \mathrm{R}=75°, \angle \mathrm{U}=120°$.

Construct the following Quadrilateral $\mathrm{DEAR}$,

$\mathrm{DE}=3 \mathrm{cm}, \mathrm{EA}=5 \mathrm{cm}, \mathrm{AR}=4.5 \mathrm{cm}, \angle \mathrm{E}=60°, \angle \mathrm{A}=90°$.

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 $\angle XAB=70°$.

How many measurements are needed to construct a square?

What are the sufficient elements to construct a unique parallelogram?

What are the sufficient elements to construct a unique rhombus?

Construct a perpendicular bisector of a line segment of $6.4 \mathrm{cm}$.

Construct a right angle using ruler and compass.

Construct an angle of which is one third of a right angle using ruler and compass.

What are the sufficient elements to construct a unique rectangle?

What are the sufficient conditions to construct a unique quadrilateral?

Construct a perpendicular bisector of a line segment of $10 \mathrm{cm}$.

Construct an angle which is one third of a straight angle using ruler and compass.

$\mathrm{AB}=6 \mathrm{cm}, \mathrm{BC}=4.5 \mathrm{cm}, \mathrm{AD}=5 \mathrm{cm}, \mathrm{AC}=6 \mathrm{cm}$ and $\angle \mathrm{D}=100°$ these five measurements are sufficient to construct a quadrilateral $ABCD$: _____ (yes/no)

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

Are these five measurements sufficient to draw a unique quadrilateral $\mathrm{ABCD}$ in which $\mathrm{AB}=6 \mathrm{cm}, \mathrm{BC}=4.5 \mathrm{cm}, \mathrm{AD}=5 \mathrm{cm}, \mathrm{AC}=6 \mathrm{cm}$ and $\angle \mathrm{D}=100°$? (Write answer as Yes or No)

It is possible to construct a quadrilateral with one side and three angles.