Practical Geometry - 8th math

Construction of a quadrilateral when two diagonals and three sides are given.

Class 8 math Practical Geometry construction of a quadrilateral when two diagonals and three sides are given solution of NCERT Exercise 4.2 Question (1) Construction of the following quadrilaterals

(i) quadrilateral LIFT

LI = 4 cm

IF = 3 cm

TL = 2.5 cm

LF = 4.5 cm

IT = 4 cm

Solution

First draw a rough sketch of the given quadrilateral to locate sides and diagonals.

Step (i) Draw a horizontal line equal to ` = 4\ cm ` to draw the given diagonal (IT = 4 cm)

Step (ii) Draw an arc of radius 2.5 cm above the diagonal IT to draw the side IL from point I. And draw an arc of radius 4 cm above the diagonal IT to draw the side TIL from point I

Step (iii) Draw line TL by joining points T and L and draw line LI by joining points I and L.

Step (iv) Now draw an arc of radius 3cm from point I below the diagonal IT. And draw another arc of radius 4.5cm from point L to cut the previous arc below the diagonal IT.

Step (v) Joint the points I and F to draw the third given side of the quadrilateral, and joint points L and F to draw the second diagonal. And finally join points T and F to draw the fourth side of the given diagonal.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry construction of a quadrilateral when two diagonals and three sides are given Solution of NCERT Exercise 4.2 Question (1) (ii) Quadrilateral GOLD

OL = 7.5 cm

GL = 6 cm

GD = 6 cm

LD = 5 cm

OD = 10 cm

Solution

First of all draw a rough quadrilateral using given measurements to get an idea of construction of quadrilateral.

Step (i) Now, draw a horizontal line to draw the diagonal GL. And cut the line equal to 6 cm using a compass and measuring scale.

Step (ii) From point L draw an arc of radius 5cm and draw another arc of radius 6cm from point G to locate the point D.

Step (iii) Joint the points L and D and G and D

Step (iv) From point L draw an arc of radius 7.5cm to draw the third side. And draw another arc of radius 10cm from point D to locate the intersection point of side LO and diagonal OD.

Step (v) Joint the points L and O to draw the third given side. And joint points D and O to draw the second diagonal. And join the points G and O to draw the fourth side to complete the quadrilateral.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry Solution of NCERT Exercise 4.2 Question (1) (iii) Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

Solution

Construction of a rhombus when measurement of both of the diagonals are given.

First of draw a rough sketch of given rhombus to locate the points and sides.

In the given rhombus diagonals are given. And on that basis rhombus is to be drawn.

Step (i) Draw a horizontal line to draw the diagonal BN and cut 5.6 cm from it.

Now, we know that diagonals of a rhombus are perpendicular bisector of one another.

This means that one diagonal bisects another one and is perpendicular to each other.

Thus, to draw the another diagonal we have to draw a perpendicular bisector of diagonal BN.

Step (ii) To draw a perpendicular bisector of BN, draw one arc above the diagonal from point B and another arc below the diagonal from point B.

Again draw one arc above the diagonal from point N and another arc below the diagonal from point N.

Step (iii) Now, join the meeting points of arc made above and below the diagonal BN. And mark the middle point of diagonals as O.

Now, since diagonal BN divides the another diagonal DE into two equal parts.

Here, the length of other diagonal DE ` = 6.5\ cm ` (as given in the question)

Thus, half of the diagonal DE` = 6.5/2 = 3.25cm `

Now draw an arc of radius ` 3.25\ cm ` above the diagonal BN on the line perpendicular to the diagonal BN. Again draw another arc of radius 3.25 cm below the diagonal BN on the line perpendicular to the diagonal BN.

Mark them D and E.

Now, join points B and D, B and E, E and N and D and N to draw sides of the given rhombus.

This is the construction of the given rhombus.

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