Construction of Triangles

As a part of a school project, Arvind and Nikita are making signboards, as shown,

Draw the triangles, $△\mathrm{ABC} \text{and} △\mathrm{PQR}$ for the given dimensions. What we do these signboards indicate?

Construct a triangle ABC in which $\mathrm{BC}=7 \mathrm{cm}$ and medians to the the other two sides are $7.8 \mathrm{cm} \text{and} 6 \mathrm{cm}.$

Construct a triangle ABC in which $\mathrm{AB}= 6 \mathrm{cm}$, median CD to AB $=4 \mathrm{cm}$ and altitude CE to AB $= 3 \mathrm{cm}$.

Is it possible to construct a triangle ABC in which $\angle \mathrm{B}={120}^{°}, \angle \mathrm{C}={60}^{°} \text{and} \mathrm{BC}=5 \mathrm{cm}$. Give reasons.

In $△\mathrm{XYZ},$ we have, $\mathrm{YZ}=7 \mathrm{cm}, \angle \mathrm{X}={45}^{°} \text{and} \angle \mathrm{Y}={60}^{°}$. Is it possible to construct the triangle?

It is possible to construct a triangle with the sides of length $2 \mathrm{cm}, 9 \mathrm{cm} \text{and} 12 \mathrm{cm}$?

Is it possible to construct a triangle with three angles ${30}^{°}, {60}^{°} \text{and} {90}^{°}.$ If not, which single detail do you need more?

Which of the following information is insufficient to construct a unique triangle?

Construct an isosceles triangle with base $4.5 \mathrm{cm}$ and vertical angle $90°$.

Construct a right-angled triangle in which one side is $5.2 \mathrm{cm}$ and hypotenuse is $6.3 \mathrm{cm}$.

Construct a triangle $DEF$, in which $\angle E=90°$ and the side containing right angle are $6.2 \mathrm{cm}$ and $5.8 \mathrm{cm}$.

Construct an isosceles triangle $ABC$ in which  $BC=5.8 \mathrm{cm}$ and base angles are $60°$. Can you give any special name to the triangle?

Using a ruler and compasses only, construct a triangle $ABC$, when $BC=7 \mathrm{cm}$, $\angle B=30°$ and  $\angle C=135°$.Measure $\angle A$

Construct a triangle $ABC$, when $\angle B=120°$, $\angle A=30°$ and  $BC=5.5 \mathrm{cm}$.

Construct a triangle $ABC$, when $\angle ABC=90°$ and $\angle ACB=45°$ and included side $BC=6.8 \mathrm{cm}$. Name the triangle.

Construct a triangle $ABC$, when $\angle ABC=60°$ and $\angle ACB=50°$ and $BC=7.2 \mathrm{cm}$

Construct a triangle $PQR$, where  $QR=5 \mathrm{cm}$, $PR=6 \mathrm{cm}$ and $\angle R=75°$. Draw the bisector of the interior angle $P$. Let the bisector meet $QR$ at $M$. Measure $QM$.

Construct a triangle $ABC$, where  $AB=5.2 \mathrm{cm}$, $BC=6.8 \mathrm{cm}$ and angle between them is $90°$.

Construct a triangle $ABC$, where  $AB=BC=5.5 \mathrm{cm}$ and $\angle ABC=120°$ .Name the triangle.

Construct a triangle $PQR$, where  $PQ=4.5 \mathrm{cm}$, $QR=5.8 \mathrm{cm}$ and the angle between them is $80°$.