Practical Geometry - 8th math

Construction of quadrilateral when two adjacent sides and three angles are known

Class 8 math Practical Geometry Construction of quadrilateral when two adjacent sides and three angles are knownSolution of NCERT Exercise 4.3 Question (1) Construct the following quadrilaterals

(i) Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60⁰

∠O = 105⁰

∠R = 105⁰

Solution

First of all construct a rough sketch of the given quadrilateral.

Step (i) First of all to draw the side MO = 6 cm. Draw a horizontal line and cut 6 cm from it using a compass and a measuring scale.

Step (ii) On the point O an angle of 105^o is made.

Step (iii) On the side OR an arc of radius 4.5 cm is drawn. This the side OR = 4.5cm

Step (iv) On point R on the side OR the given angle 105^o is made.

Step (v) Now, draw an angle equal to 60^o on point M and stretch the line upto ray of angle made on point R to complete the given quadrilateral.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry Construction of quadrilateral Solution of NCERT Exercise 4.3 Question (1) (ii) Quadrilateral PLAN

PL = 4 cm

LA 6.5 cm

∠P = 90^o

∠A = 10^o

∠N = 85^o

Solution

First of all a rough sketch of the given quadrilateral is drawn to estimate the construction.

Here, since angle L is not given thus, without knowing the angle L it is not possible to draw the given quadrilateral because ∠L is the angle made between given adjacent sides.

Now, we know that, sum of measure of angles of a quadrilateral = 360⁰

Thus, 85^o + 90^o + ∠L + 110^o = 360^o

⇒ 285^o + ∠L = 360^o

⇒ ∠L = 360^o – 285^o

Step (i) Draw a horizontal line and cut it equal to 4 cm using a compass and a measuring scale.

Step(ii) Make an angle equal to on point L and draw a line for this angle.

Step (iii) Measure a length of cm using a compass and scale and make an arc of this radius 6.5 cm on side LA.

Step (iv) Draw and angle equal to 110^o on point A and draw a line for this angle.

Step (v) Draw an angle equal to 90^o on point P. And draw a line which meets on point N, i.e. AN to complete the given quadrilateral.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry Construction of quadrilateral Solution of NCERT Exercise 4.3 Question (1) (iii) Parallelogram HEAR

HE = 5 cm

EA = 6 cm

∠R = 85⁰

Solution

First of all a rough sketch of the given parallelogram is drawn to estimate the construction of given parallelogram.

Here, as given ∠R = 85^o

And we know that, opposite angles of a parallelogram are equal in measurement.

Here, since ∠E is the opposite angle of ∠R

Thus, ∠E = ∠R

Thus, ∠E = 85^o

Now, we know that, the sum of adjacent angles of a parallelogram is equal = 180^o

Thus, ∠R + ∠H = 180^o

⇒ 85^o + ∠H = 180^o

⇒ ∠H = 180^o – 85^o

⇒ ∠H = 95^o

Step (i) To draw the side HE = 5 cm of the given parallelogram, a horizontal line is drawn and cut it using a compass and measuring scale equal to 5 cm.

Step (ii) Angle E = 85^o is drawn on point E using a protector.

Step (iii) And using a compass an arc of radius 6 cm is made on the ray of angle made on point E

Step (iv) Mark an arc of radius 6 cm on the ray coming out from the point E at an angle of 85^o. And name this point as A.

Step (v) Draw and angle equal to 95^o on point H and draw a line for this angle.

Since AE||HR

And, we know that the opposite sides of a parallelogram are equal in measure.

Thus, HR = EA = 6 cm

Step (vi) Mark an arc of radius 6cm on line coming out from the point H. Name this point as R.

Step (vii) Now draw a line to connect point R and A to complete the given quadrilateral.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry Construction of quadrilateral Solution of NCERT Exercise 4.3 Question (1) (iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

Solution

First of all a rough sketch of the given rectangle is made to estimate the construction.

We know that, a rectangle has all angles equal to 90^o. And opposite sides are equal.

Step (i) Draw a horizontal line and cut it equal to 7 cm using a compass and a measuring scale.

Step (ii) Draw an angle equal to 90^o at point K and draw a line for this angle.

Step (iii) Draw and arc of radius 5 cm on the line of the angle of 90^o made on point K. And mark the point of arc meeting at line as A. This is side KA = 5cm.

Step (iv) Draw an angle equal to 90^o at point P and draw a line for this angle. Because in a rectangle opposite sides are parallel and angle made by the side of rectangle is equal to 90^o.

Step (v) Draw and arc of radius 5 cm on the line of the angle of 90^o made on point O. And mark the point of arc meeting at line as Y. This is side OY = 5cm. Because opposite side of a rectangle are equal.

Step (vi) Join the point Y and A and complete the rectangle. This is side YA = 7cm

This is the construction of given rectangle.