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Standard VIII

Mathematics

Construction of a Quadrilateral When Two Diagonals and Three Sides Are Given

A quadrilater...

Question

A quadrilateral ABCD has AB = 7 cm, BC = 4 cm, CD = 5 cm, ∠B = 80^o and ∠C = 100^o. To construct the quadrilateral ABCD, the first step is to draw AB = 7 cm. Which of the following will be the second step?

Draw CD = 5 cm.

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Draw a ray ABX making an angle of 80^o.

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Draw a ray ABX making an angle of 100^o

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Draw BC = 4 cm

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Solution

The correct option is B
Draw a ray ABX making an angle of 80^o.

For the given quadrilateral ABCD, we know the measurements of its three sides and two included angles.

To construct the quadrilateral ABCD, after drawing the line segment BC of length 7 cm, the next step would be to construct angle ABX equal to 80^o.

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Similar questions

Can we draw a quadrilateral ABCD with following measurements: AB = 3cm, BC = 5cm, AD = 4cm, CD= 7cm and BD=8cm?

Q. To construct a trapezium ABCD with

A B ∥ C D,

AB = 6.5 cm, BC = 6.2 cm,

∠ A B C = 80^{\circ}

and

∠ D A B = 105^{\circ},

we follow the following steps:
1) Draw the line segment AB = 6.5 cm.
2) Construct the angle

∠ A B X = 80^{\circ}

at B.
3) With B as centre, draw an arc of radius 6.2 cm cutting BX at C.
4) Draw CD parallel to AB.
The next step involved in the construction is __.

Try to draw quadrilateral ABCD of these specifications:

(i) AB = 7 cm, BC =5 cm, CD = 4 cm, ∠B = 60°, ∠C = 140°.

(ii) AB = 8 cm, BC = 6 cm, CD = 5.5 cm, DA = 3 cm, ∠B = 50°.

(iii) AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm.

Q. For construction of a quadrilateral

A B C D

, where

A B = 4.2

cm,

B C = 3.8

cm,

C D = 4.9

cm,

A D = 5.4 c m

and

∠ B = 72

. Its steps for construction is given in jumbled form. Identify the second step from the following:
1) From

B

, set off

B C = 3.8

cm.
2) Draw

A B = 4.2

cm and Make

∠ A B X = 72^{\circ}

.
3) With

A

as center and radius equal to

5.4

cm draw an arc.
4) With

C

as center and radius equal to

4.9

cm, draw another arc, cutting the previous arc at

D

. Join

A D

and

C D

Q. Construct a quadrilateral

A B C D

in which

A B = 3.6 cm, ∠ A B C = 80^{\circ}, B C = 4 cm, ∠ B A D = 120^{\circ}

, and

A D = 5 cm

.
Steps of construction are:
(i) Make

∠ B A Y = 120^{\circ}

(ii) Join

C D

(iii) With

B

as centre and radius equal to

4 cm

, draw an arc, cutting

B X

C

.
(iv) Draw

A B = 3.6 cm

(v) With

A

as centre and

5 cm

as radius, draw an arc, cutting

A Y

D

.
(vi) Make

∠ A B X = 80^{\circ}

Choose the correct order of steps of construction.

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A quadrilateral ABCD has AB = 7 cm, BC = 4 cm, CD = 5 cm, ∠B = 80o and ∠C = 100o. To construct the quadrilateral ABCD, the first step is to draw AB = 7 cm. Which of the following will be the second step?

A quadrilateral ABCD has AB = 7 cm, BC = 4 cm, CD = 5 cm, ∠B = 80^o and ∠C = 100^o. To construct the quadrilateral ABCD, the first step is to draw AB = 7 cm. Which of the following will be the second step?