Telangana Board Solutions for Chapter: Construction of Quadrilaterals, Exercise 1: Exercise 1

A student attempted to draw a quadrilateral $\mathrm{PLAY}$ given that $\mathrm{PL}=3 \mathrm{cm}$, $\mathrm{LA}=4 \mathrm{cm}$, $\mathrm{AY}=4.5 \mathrm{cm}$, $\mathrm{PY}=2 \mathrm{cm}$ and $\mathrm{LY}=6 \mathrm{cm}$. But he was not able to draw it why? Try to draw the quadrilateral yourself and give reason.

Can you draw the quadrilateral $\mathrm{ABCD}$ (given above) by constructing $△\mathrm{ABD}$ first and then fourth vertex $\text{'}\mathrm{C}\text{'}$? Give reason.

Construct a quadrilateral $\mathrm{PQRS}$ with $\mathrm{PQ}=3 \mathrm{cm}$, $\mathrm{RS}=3 \mathrm{cm}$, $\mathrm{PS}=7.5 \mathrm{cm}$, $\mathrm{PR}=8 \mathrm{cm}$ and $\mathrm{SQ}=4 \mathrm{cm}$. Justify your result.

Can you construct the above quadrilateral $\mathrm{PQRS}$, if we have an angle of $100°$ at $\mathrm{P}$ instead of $75°$ Give reason.

(Draw a rough sketch in each case and analyse the figure) State the reasons for your conclusion.

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 $\angle \mathrm{A}=140°$ .

(Draw a rough sketch in each case and analyse the figure) State the reasons for your conclusion

Do you construct the above quadrilateral $\mathrm{ABCD}$ by taking $\mathrm{BC}$ as base instead of $\mathrm{AB}$? If So, draw a rough sketch and explain the various steps involved in the construction.

Can you construct the above quadrilateral (rhombus) taking $\mathrm{BD}$ as a base instead of $\mathrm{AC}$? If not give reason.

Suppose the two diagonals of this rhombus are equal in length, what figure do you obtain? Draw a rough sketch for it. State reasons.