Ncert Solutions For Class 8 Maths Ex 4.3

Question 1:

 Construct the quadrilaterals.

(i) Quadrilateral EROM

Side MO = 6cm

Side OR = 4.5cm

$\angle M=60^{\circ}$

$\angle O=105^{\circ}$

$\angle R=105^{\circ}$

(ii)Quadrilateral NALP

PL = 4cm

LA = 6.5cm

$\angle P=90^{\circ}$

$\angle A=110^{\circ}$

$\angle N=85^{\circ}$

(iii)Parallelogram RAEH

EH = 5cm

AE = 6cm

$\angle R=85^{\circ}$

(iv) Rectangle YAKO

KO = 7cm

AK = 5cm

 

Answer:

(i)

(1) Sketch the figure of the quadrilateral

(2) Using the geometry tools draw the line segment OM 6cm and an angle of $105^{\circ}$ at point O. As vertex R is 4.5cm away from the vertex O, cut a line segment RO of 4.5cm from this ray.

(3) Again, draw an angle of $105^{\circ}$ at point R.

(4) Draw an angle of $60^{\circ}$ at point M. Extend this ray so that it meets the previously drawn from R at point E.

EROM is the desired quadrilateral.

 

(ii)

(1) Total sum of the interior angles of quadrilateral is $360^{\circ}$

In quadrilateral NALP, $\angle P+\angle L+\angle A+\angle N=360^{\circ}$

$90^{\circ}+\angle L+110^{\circ}+85^{\circ}=360^{\circ}$ $285^{\circ}+\angle L=360^{\circ}$ $\angle L=360^{\circ}-285^{\circ}=75^{\circ}$

(2)Draw a rough diagram of quadrilateral

(3) Construct a line PL of 4cm and draw an angle of $75^{\circ}$ at point L. As vertex A is 6.5cm away from vertex L, cut a line segment LA of 6.5cm from this ray.

(4) Draw another angle of $110^{\circ}$ at point A.

(5) Construct an angle of $90^{\circ}$ at point P. This line will meet touch the previously drawn ray from A at point N.

NALP is the required quadrilateral

 

(iii)

(1)Sketch a rough diagram of this quadrilateral as follows

(2)Construct a line segment EH of 5cm and an angle $85^{\circ}$ at point E. As vertex A is at a distance of 6cm and 5cm, draw arcs from point H and A respectively. These will be intersecting each other at point R.

(3) Vertex H and A are 6 and 5cm away from vertex R. By taking radius as 6cm and 5cm, draw arcs from point H and A respectively. These will be intersecting each other at point R.

(4) Join H and A with point R

RAEH is the desired quadrilateral.

 

(iv)

(1) Draw a rough diagram of this quadrilateral as follows.

(2) Construct a line segment KO of 7cm and an angle of $90^{\circ}$ at point K. As vertex A is 5cm away from vertex K, cut a line segment AK of 5cm from this ray.

(3) Draw two arcs of radius 5 cm from points O and K respectively. These arcs intersect at Y and A.

(4) Join AY

It is the desired rectangle YAKO