West Bengal Board Solutions for Chapter: Geometrical Concepts Based on Different Instruments of Geometry Box., Exercise 20: Exercise 20

Sayan place two No. $2$ set squares together along the edges, to get a shape given below by drawing the figure with pencil on his exercise book.

It is observed that the diagram traced with pencil is a quadrilateral and is named as $ABCD$.

But this quadrilateral is a rectangle, since, by measuring its sides with a scale, it is found,

$AB$ _____ $CD [=/>/<]$ and $AD$ _____ $BC [=/>/<]$

$\angle ABC=\angle BCD=\angle CDA=\angle DAB=$ _____

Again, it is found by measurement that $AC$ _____ $BD [=/>/<]$.

Sahana place two OIJ=set squares together along the edges, as shown in the diagram below. She traced the shape formed by set squares, in her exercise book and named it $PQRS$.

By tracing the diagram formed with two No.$1$ set squares, the figure formed is a quadrilateral. This quadrilateral is a square $PQRS$.

The four sides of the square were measured with scale, $PQ=$ _____, $QR=$ _____, $RS=$ _____ and $SP=$ _____.

Hence, it is verified that the length of each side of a square are _____ [equal/unequal].

Again, $\angle PQR=\angle QRS=\angle RSP=\angle SPQ=$ _____.

$\angle PQR+\angle QRS+\angle RSP+\angle SPQ=$ _____ $+$ _____ $+$ _____ $+$ _____ $=$ _____.

Again, the line segments $PR$ and $QS$ are measured. It is found that te lengths of the line segments $PR$ and $QS$ are _____ [equal/unequal].

Kushal wanted to form a rectangular shape like Sayan's with two No. $2$ set squares. But by mistake he placed the set squares with different edge together, hence he got a diagram as given below. By tracing the diagram with pencil in his exercise book, he got a different figure.

He found the figure a quadrilateral. He named it $EFGH$.

Now, it is found that in quadrilateral $EFGH, EF\parallel HG$ and $EH\parallel FG$.

That is, in quadrilateral $EFGH$, the opposite sides are _____ [parallel/intersecting].

By measurement, it is found that the opposite sides of the parallelogram are _____ [equal/unequal].

$\angle EFG=$ _____, $\angle FGH=$ _____, $\angle GHE=$ _____ & $\angle HEF=$ _____

Hence, the opposite angles are _____ [equal/unequal].

$EG$ _____ $HF$ [$=/>/<$] (By measurement].

Again, $\angle EFG+\angle FGH+\angle GHE+\angle HEF=$ _____ $+$ _____ $+$ _____ $+$ _____ $=360°$.

We four of us, put our No. $1$ set square i.e. $4$ set square of $30°-60°-90°$ together and traced the boundary on the paper and let us see, what we get.

We got a quadrilateral $UVWX$.

By measurement, it is found that, the lengths of the sides $UV, VW, WX, XU$ are _____ [equal/unequal].

Measure, to get, $UW$ _____ $XV$ [$=/>/<$]

Measuring the angles with a protractor, we found

$\angle UVW=$ _____, $\angle VWX=$ _____, $\angle WXU=$ _____ & $\angle XUV=$ _____

In the quadrilateral $UVWX$, opposite angles are _____ [equal/unequal].

Again, $\angle UVW+\angle VWX+\angle WXU+\angle XUV=$ _____.