Practical Geometry - 8th math

Draw the following

Class 8 math Practical Geometry Construction of quadrilateral Solution of NCERT Exercise 4.5 Question (1) The square READ with RE = 5.1 cm

Solution

We know that all the four sides of a square are equal in measurement and all of the four angles are equal to 90^o.

Here measurement of one side RE is given, thus all the side will be equal to RE = 5.1 cm

Step (i) Draw a horizontal line and cut from it. And name it RE.

Step (ii) Draw an angle of 90^o on point E of the side RE. And cut 5.1 cm for it to draw the side

Step (iii) Draw an angle of 90^o on point R of the side RE. And cut 5.1 cm for it to draw the side DR = 5.1 cm.

Step (iv) Join points D and A to draw the fourth side of the given quadrilateral.

This is the construction of the given quadrilateral.

Class 8 math Practical Geometry Construction of quadrilateral Solution of NCERT Exercise 4.5 Question (2) A rhombus whose diagonals are 5.2 cm 6.4 cm long.

Solution

Here diagonals of the rhombus are given which is equal to 5.2 cm and 6.4 cm long.

We know that, diagonals of a rhombus are perpendicular bisectors of one another.

Here given first diagonal

And second diagonal = 5.2 cm

Thus, half of the second diagonal cm

Step (i) Draw a horizontal line and cut 6.4 cm from it to draw the one diagonal. Mark it as AB.

Step (ii) Draw a perpendicular bisector of diagonal AB

Step (iii) Now, draw an arc of radius above the diagonal AB and one arc of radius 2.6 cm below the diagonal AB. And mark those points as C and D

Step (iv) Join the points A and C, points B and C, points A and D and points D and B to complete the quadrilateral.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry Construction of quadrilateral Solution of NCERT Exercise 4.5 Question (3) A rectangle with adjacent sides of length 5 cm and 4 cm.

Solution

Given, adjacent sides of the rectangle are 5 cm and 4 cm respectively.

We know that, opposite sides of a rectangle are equal and angles made by adjacent sides are right angle.

Step (i) Draw a horizontal line and cut 5 cm from it to draw one side of the given quadrilateral. Name it AB.

Step (ii) Draw an angle equal to at point B. And cut 4 cm from it to draw the adjacent side.

Step (iii) Draw an angle equal to 90^o at point A. And cut 4 cm from it to draw the adjacent side.

Step (iv) Now join points D and C to draw the fourth side and parallel side to AB and complete the construction.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry Construction of quadrilateral Solution of NCERT Exercise 4.5 Question (4) A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

Solution

Given two sides of parallelogram, and

We know that, parallel sides of a parallelogram are equal thus other two sides will have same measurement.

Since angles of the adjacent sides of the parallelogram are not given, thus it is assumed that given parallelogram is a rectangle.

Step (i) Draw a horizontal line to draw side OK of the parallelogram. And cut 5.5 cm from it.

Step (ii) Draw an angle equal to 90^o on point K and extend the line. And cut 4.2 cm from it to draw the adjacent side of the given parallelogram KA.

Step (iii) Draw an angle equal to 90^o on point O and extend the line. And cut 4.2 cm from it to draw the adjacent side of the given parallelogram OY.

Step (iv) Now, join points Y and A to draw the side YA which is parallel to side OK and complete the construction of given parallelogram.

This is the construction of given quadrilateral.