# Construction of Quadrilaterals

Chapters

- ap-scert-8th-class-Maths-Lesson-1-Rational-Numbers
- ap-scert-8th-class-Maths-Lesson-4-Exponents-and-Powers
- ap-scert-8th-class-Maths-Lesson-10-Direct-and-Inverse-Proportions
- ap-scert-8th-class-Maths-Lesson-2-Linear-Equations-in-One-Variable
- ap-scert-8th-class-Maths-Lesson-3-Construction-of-Quadrilaterals
- ap-scert-8th-class-Maths-Lesson-6-Square-Roots-and-Cube-Roots
- ap-scert-8th-class-Maths-Lesson-7-Frequency-Distribution-Tables-and-Graphs
- ap-scert-8th-class-Maths-Lesson-8-Exploring-Geometrical-Figures
- ap-scert-8th-class-Maths-Lesson-9-Area-of-Plane-Figures
- ap-scert-8th-class-Maths-Lesson-11-Algebraic-Expressions
- ap-scert-8th-class-Maths-Lesson-12-Factorisation
- ap-scert-8th-class-Maths-Lesson-13-Visualizing-3-D-in-2-D
- ap-scert-8th-class-Maths-Lesson-14-Surface-Areas-and-Volume-(Cube-Cuboid)
- ap-scert-8th-class-Maths-Lesson-15-Playing-with-Numbers

- ap-scert-8th-class-Maths-Lesson-1-Rational-Numbers
- ap-scert-8th-class-Maths-Lesson-4-Exponents-and-Powers
- ap-scert-8th-class-Maths-Lesson-10-Direct-and-Inverse-Proportions
- ap-scert-8th-class-Maths-Lesson-2-Linear-Equations-in-One-Variable
- ap-scert-8th-class-Maths-Lesson-3-Construction-of-Quadrilaterals
- ap-scert-8th-class-Maths-Lesson-6-Square-Roots-and-Cube-Roots
- ap-scert-8th-class-Maths-Lesson-7-Frequency-Distribution-Tables-and-Graphs
- ap-scert-8th-class-Maths-Lesson-8-Exploring-Geometrical-Figures
- ap-scert-8th-class-Maths-Lesson-9-Area-of-Plane-Figures
- ap-scert-8th-class-Maths-Lesson-11-Algebraic-Expressions
- ap-scert-8th-class-Maths-Lesson-12-Factorisation
- ap-scert-8th-class-Maths-Lesson-13-Visualizing-3-D-in-2-D
- ap-scert-8th-class-Maths-Lesson-14-Surface-Areas-and-Volume-(Cube-Cuboid)
- ap-scert-8th-class-Maths-Lesson-15-Playing-with-Numbers

- Solutions
- PDF Download
- Question Papers
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Solutions

Quadrilateral ABCD with AB = 5.5 cm, BC = 3.5 cm, CD = 4 cm, AD = 5 cm and ∠A = 45°.

Solution:

In Quadrilateral ABCD with AB = 5.5 cm, BC = 3.5 cm, CD = 4 cm, AD = 5 cm and ∠A = 45°.

Quadrilateral BEST with BE = 2.9 cm, ES = 3.2 cm, ST = 2.7 cm, BT = 3.4 cm and ∠B=75°.

Solution:

In Quadrilateral BEST

BE = 2.9 cm, ES = 3.2 cm, ST = 2.7 cm, BT = 3.4 cm and ∠B=75°.

Parallelogram PQRS with PQ = 4.5 cm, QR =3 cm and ∠PQR = 60°.

Solution:

In a parallelogram PQRS

PQ = 4.5 cm, QR = 3 cm, ZPQR = 60°.

=RS4.5cmzPS=3crn

[: Opposite sides of a I)aralielograrn are equal]

Construction Steps:

- Draw a line segment ¡i with radius 4.5 cm.
- With the centre Q draw a ray and an arc equal to 60° and 3 cm.
- The intersecting point of these two keep as R’.
- With the centres R, P draw arcs with 4.5 cm, 3 cm respectively. Keep ‘S’ as the intersecting point of these two arcs.
- Join P, S and R, S.
- ∴ The required parallelogram PQRS is formed.

Rhombus MATH with AT =4 cm, ∠MAT =120°.

Solution:

Rectangle FLAT with FL =5 cm, LA= 3 cm.

Solution:

In a rectangle FLAT

FL=AT=5cm, LA = TF = 3cm, ∠F = ∠L = ∠A = ∠T = 90°

Square LUDO with LU = 4.5 cm.

Solution:

In a square LUDO

LU = UD = DO = OL = 4.5 cm

∠L = ∠U = ∠D = ∠O = 90°

Quadrilateral ABCD with AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm andAC= 7cm

Solution:

In Quadrilateral ABCD with AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm and AC = 7 cm.

- With the centres A, B draw arcs equal to 7 cm and 5.5 cm respectively. The intersection of these two arcs keep as ‘C’.
- Join A, C and B, C.
- With centres C, A draw arcs equal to 4 cm, 6 cm respectively. These intersecting point is keep as ’D’.

Join D, C and A, D. - ∴ The required quadrilateral ABCD is formed.

Quadrilateral PQRS with PQ = 3.5 cm, QR = 4 cm, RS = 5 cm, PS = 4.5 cm and QS= 6.5 cm

Solution:

In a quadrilateral PQRS,

PQ = 3.5 cm, QR = 4 cm, RS = 5 cm,

PS - 4.5 cm, QS = 6.5 cm

- With the centres P, Q draw arcs equal to 4.5 cm and 6.5 cm respectively.
- These two arcs meet at point ‘S’.
- With the centres S, Q draw arcs with radius 5 cm, 4 cm respectively. These two arcs intersected at point ‘R’.
- Join P, S; Q, S; S, R and Q, R.
- ∴ The required quadrilateral PQRS is formed.

Parallelogram ABCD with AB = 6cm, CD = 4.5 cm and BD = 7.5 cm

Solution:

In a parallelogram ABCD; AB = 6 cm, BC = 4.5 cm, BD = 7.5 cm

AB = CD (;cm

BC = AD = 4.5 cm

BD = 7.5 cm

- With the centres A, B draw arcs with radius 4.5 cm, 7.5 cm respectively. These two arcs meet at point ‘D’.
- With the centres D, B draw arcs with radius 6 cm, 4.5 cm respectively. These two arcs meet at point ‘C’.
- Join A, D and B, C and D, C and B, D.
- ∴ The required parallelogram ABCD is formed.

Rhombus NICE with NI = 4 cm and IE = 5.6 cm

Solution:

In a rhombus NI = IC = CE = NE = 4 cm, IE = 5.6 cm

- With the centres N, I draw two arcs with radius 4 cm, 5.6 cm respectively. These two arcs meet at point E’.
- With the centres E, I draw arcs with radius 4 cm. These two arcs meet at point ‘C’.
- Join N, E and I, E. Also join E, C and I, C.
- .’. The required rhombus NICE is formed.

Quadrilateral GOLD: OL = 7.5 cm, GL = 6 cm, LD = 5 cm, DG = 5.5 cm and OD = 10 cm.

(Ex 3.3, Page No. 72)

Solution:

In a quadrilateral GOLD, Rough Diagram

OL = 7.5 cm, GL = 6 cm

LD = 5 cm, DG = 5.5 cm, OD = 10 cm

- With the centres O, L draw arcs with radius 10 cm and 5 cm respectively. These two arcs meet at point ‘D’.
- With the centres L, D draw arcs equal to 6 cm and 5.5 cm respectively. These two arcs meet at point ‘G’.
- Join O, G and L, G. Also join O, D and L, D and G, D.
- ∴ The required quadrilateral GOLD is formed.

Quadrilateral PQRS: PQ = 4.2 cm, QR = 3 cm, PS = 2.8 cm, PR = 4.5 cm and QS = 5 cm.

Solution:

In a quadrilateral PQRS

PQ = 4.2 cm PS = 2.8 cm

QR = 3 cm PR = 4.5 cm

QS = 5 cm

- With the centres P, Q draw arcs equal to the radius 4.5 cm, 3 cm respectively. These two arcs meet at point R’. Join P, R and Q, R.
- With the centres Q, P draw arcs equal to the radii 5 cm and 2.8 cm respectively. These two arcs meet at point ‘S’.
- Join P, S and Q, S and S, R.
- ∴ The required PQRS quadrilateral is formed.

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