ICSE Class 7 Maths Chapter 28 Construction of Quadrilaterals

Chapter 28: Construction Of Quadrilaterals

Construction Of A Quadrilateral ABCD

A quadrilateral has four vertices and to construct a quadrilateral means to locate the positions of these four vertices.

When Four Sides And One Diagonal Are Given

Let AB = 3.5 cm, BC = 4.5 cm, CD = 4 cm, DA = 5.5 cm and diagonal AC = 5 cm.

Steps

1. Draw AB = 3.5 cm.

2. With A as centre, draw an arc of length 5 cm, (AC) and with B as centre, draw an arc of length 4.5 cm (BC). These two arcs meet at C.

3. With C as centre, draw an arc of radius 4 cm (CD) and with A as centre, draw one more arc of radius 5.5 cm (DA). These two arcs cut each other at point D.

4. Join BC, CD and AD.

Then, ABCD is the required quadrilateral.

Teacher's Note

Understanding how to construct quadrilaterals with given measurements helps in practical applications like land surveying and architectural planning.

When Three Consecutive Sides And Two Included Angles Are Given

Let AB = 5 cm, AD = 4 cm, BC = 5.5 cm, angle BAD = 60° and angle ABC = 90°.

Steps

1. Draw AB = 5 cm.

2. At A, draw angle BAY = 60°.

3. At B, draw angle ABX = 90°.

4. From BX, cut BC = 5.5 cm.

5. From AY, cut AD = 4 cm.

6. Join C and D.

Then, ABCD is the required quadrilateral.

Teacher's Note

Angle measurements are crucial in construction and design, similar to how carpenters and engineers use angles to create furniture and buildings.

Construction Of A Parallelogram ABCD

When Two Consecutive Sides And An Included Angle Are Given

Let BC = 4.2 cm, CD = 3.6 cm, and angle BCD = 60°.

Students know that the opposite sides of a parallelogram are equal. Therefore, BC = 4.2 cm = AD and CD = 3.6 cm = AB.

Steps

1. Draw BC = 4.2 cm.

2. At C, construct angle PCB = 60° and from CP cut CD = 3.6 cm.

3. Taking D as centre, draw an arc of radius 4.2 cm (AD) and taking B as centre, draw an arc of radius 3.6 cm (AB). Let the two arcs intersect each other at point A.

4. Join AB and AD.

Then, ABCD is the required parallelogram.

Teacher's Note

Parallelograms appear in everyday objects like window frames and parallelogram-shaped tiles used in construction and design.

When Two Consecutive Sides And One Diagonal Are Given

Let AB = 4.5 cm, BC = 4.7 cm and the diagonal AC = 6.2 cm.

Steps

1. Draw AB = 4.5 cm.

2. Taking B as centre, draw an arc of radius 4.7 cm (= BC) and taking A as centre, draw one more arc of radius 6.2 cm (= diagonal AC). Let the two arcs intersect each other at the point C.

3. Join B and C.

4. Taking C as centre, draw an arc of radius 4.5 cm (= AB) and taking A as centre, draw one more arc of radius 4.7 cm (= BC). Let these arcs intersect each other at the point D.

5. Join AD and CD.

Then, ABCD is the required parallelogram.

Teacher's Note

The diagonal method is useful in engineering when one measurement is already fixed and you need to complete a parallel structure around it.

Construction Of A Rectangle ABCD

When Two Adjacent Sides Of A Rectangle Are Given

Let AB = 5 cm and BC = 3.5 cm.

Steps

1. Draw AB = 5 cm.

2. At B, draw BX perpendicular to AB, i.e., angle ABX = 90°.

3. With B as centre, draw an arc of 3.5 cm radius which cuts BX at the point C.

4. With C as centre, draw an arc of 5 cm radius and with A as centre, draw another arc of 3.5 cm radius.

These two arcs cut each other at the point D.

5. Join AD and CD.

Then, ABCD is the required rectangle.

Teacher's Note

Rectangles are the most common shape in building design, from room dimensions to window and door frames in our homes.

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