Practical Geometry - 8th math

Construction of Quadrilaterals when the lengths of four sides and a diagonal are given.

Class 8 math Practical Geometry solution of NCERT Exercise 4.1 Question (1) Construct the following quadrilaterals.

(i) Quadrilateral ABCD

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

Solution

Before doing construction draw a rough sketch of the given quadrilateral to estimate its construction.

Here to construct the given quadrilateral measure of four sides and one of the diagonal is given.

To construct such quadrilateral first of all diagonal is constructed and then all the four sides are constructed.

Step (i) Draw a horizontal line

Step (ii) Cut 7 cm from this horizontal line using compass and pencil by making two arcs.

This is diagonal of the quadrilateral, given the name AC to this diagonal.

Step (iii) As given in question, ` AD = 6 cm `; draw an arc using compass at a distance of 6cm from point A.

Step (iv) As given in question, `CD = 4 cm`; draw another arc or radius 4cm using compass from point C. These arcs cut the previously drawn arc at a point. This point is D

Step (v) Now, draw a line to join points D and C.

Step (vi) Now, draw line to join points A and D

Step (vii) Now, draw an arcs of radius `4.5 cm` from A and another arc of radius `5.5 cm` from point C to draw AB and BC

Step (viii) Now draw a line to join points C and B

Step (ix) Now draw a line to join points A and B

And write the measurement of all the sides.

This is the construction of given quadrilateral.

Class 8 math Practical Geometry solution of NCERT Exercise 4.1 Question (1) (ii) Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

Solution

In the given question, diagonal and four sides of the quadrilateral are given.

When diagonal and other four sides of a quadrilateral are given, then to construct the quadrilateral first of all diagonal is drawn and then other sides.

Here PU = 6.5 cm is the diagonal of the given quadrilateral.

Before doing construction first draw a rough sketch of given quadrilateral to estimate its drawing.

Step(i) Draw a vertical straight line to draw the diagonal and cut 6.5cm from it by making two arcs of radius 6.5cm from point P and U.

Step(ii) Measure Um = 4cm and MP = 5cm and mark them using compass on the right side of the diagonal by making two arcs.

Step(iii) Join UM and MP

Step (iv) Measure JU = 3.5cm and PJ = 4.5cm using a compass and measuring scale and draw two arcs one by one on the right side of the diagonal from point P and U.

Step (v) Join JU and PJ to complete the given quadrilateral.

This is now the construction of the given quadrilateral.

Class 8 math Practical Geometry solution of NCERT Exercise 4.1 Question (1) (iii) Parallelogram MORE

OR = 6cm

RE = 4.5cm

EO = 7.5cm

Solution

Here two parallel sides and one diagonal of the parallelogram is given.

Parallel side (i) = OR = 6 cm

Parallel side (ii) = RC = 4.5 cm

And diagonal = EO = 7.5 cm

Now, since one of the diagonals and two parallel sides are given to construct a parallelogram. Thus fist of all diagonal is drawn and then other four sides.

Before doing construction draw a rough sketch of the given quadrilateral to estimate its construction.

Step (i) Draw a horizontal line to draw the diagonal and cut 7.5 cm from it using a compass and a measuring scale by making two arcs one from point O and another from point E.

Step (ii) Mark one of the parallel side EM = 6 cm and other parallel side OM = 4.5 cm above the diagonal using a compass and a measuring scale and name this point as M by making two arcs one from point O and another from point E.

Step (iii) Join the line EM and OM

Step (iv) Mark one of the parallel side OR = 6 cm and other parallel side ER = 4.5 cm below the diagonal using a compass and a measuring scale and name this point as R by making two arcs one from point O and another from point E.

Step (v) Join the line OR and ER and mark the measurements of the lines.

This is the construction of given parallelogram.

Class 8 math Practical Geometry solution of NCERT Exercise 4.1 Question (1) (iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Solution

Given, side of rhombus = 4.5 cm

And one of the diagonal (ET) = 6cm

Here since sides of a rhombus are equal, thus measurement of each side = 4.5 cm

Since one of the diagonals is given, thus first of all diagonal is drawn and then sides of the rhombus will be drawn.

Step (i) Draw a horizontal line to draw one of the diagonal and cut 6cm from it using a compass and a measuring scale.

Step (ii) Measure 4.5cm using compass and a measuring scale and mark from point E and from point T above the line ET to draw two sides of the given rhombus. And name it B.

Step(iii) Joint the points B and T and again join the points E and B to draw two sides of the given rhombus.

Step (iv) Measure 4.5cm using compass and a measuring scale and mark from point E and from point T below the line ET to draw the other two sides of the given rhombus. And name it S.

Step (v) Now, join the points S and T and E and S to draw the two other sides of the given rhombus. Now mark the measurements and to complete the construction of the given rhombus.

This is the construction of the given rhombus.

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