CBSE Class 8 Mathematics Practical Geometry Assignment Set 05

VIII - Mathematics Assignment No - 03 - Practical Geometry
Construct the following constructions and write their steps of construction.

Question 1. Construct a quadrilateral ABCD such that AB = 5 cm, BC = 5 cm, angle ABC = 80 degrees, AD = 5.5 cm and CD = 6 cm.
Answer:
Steps of Construction:
1. Draw a line segment AB = 5 cm.
2. At point B, construct an angle of 80 degrees using a protractor, i.e., angle ABX = 80 degrees.
3. With B as center and radius 5 cm, draw an arc intersecting ray BX at point C. Join BC.
4. With A as center and radius 5.5 cm, draw an arc.
5. With C as center and radius 6 cm, draw another arc intersecting the previous arc at point D.
6. Join AD and CD.
ABCD is the required quadrilateral.
In simple words: Draw a base line, construct the given angle at one end, mark the side lengths with a compass, and complete the four-sided shape by connecting the final point.

Exam Tip: Always make a rough sketch first to understand the relative position of sides and angles before doing the final construction.

Question 2. Construct a rhombus ABCD such that one side is 5 cm and one diagonal is 8 cm.
Answer:
Steps of Construction:
1. Draw a line segment AB = 5 cm.
2. With A as center and radius equal to the diagonal length (8 cm), draw an arc.
3. With B as center and radius 5 cm (since all sides of a rhombus are equal), draw an arc intersecting the previous arc at point D.
4. Join AD and BD.
5. Now, with D as center and radius 5 cm, draw an arc.
6. With B as center and radius 5 cm, draw another arc intersecting at point C.
7. Join CD and BC.
ABCD is the required rhombus.
In simple words: Use the property that all sides of a rhombus are equal, construct triangle ABD first using SSS criterion, and then complete the rhombus by drawing intersecting arcs for the fourth vertex C.

Exam Tip: Remember that all four sides of a rhombus are equal in length, which helps in setting your compass radius correctly.

Question 3. Construct a parallelogram PQRS such that PQ = 6 cm, PS = 5 cm and the distance between parallel sides PQ and SR is 4 cm.
Answer:
Steps of Construction:
1. Draw a line segment PQ = 6 cm.
2. At any point on PQ, construct a perpendicular of height 4 cm (the distance between parallel sides).
3. Draw a line parallel to PQ at a distance of 4 cm.
4. With P as center and radius 5 cm, draw an arc intersecting the parallel line at point S.
5. Join PS.
6. With S as center and radius 6 cm (since opposite sides are equal), draw an arc on the parallel line. With Q as center and radius 5 cm, draw an arc intersecting at point R.
7. Join SR and QR.
PQRS is the required parallelogram.
In simple words: Draw the base, set up a parallel line at the given height, mark the side length to find the third vertex, and complete the parallelogram using opposite side lengths.

Exam Tip: The distance between parallel sides is always measured along a perpendicular line segment drawn between them.

Question 4. Construct a square DEAR such that one of its side is 5 cm.
Answer:
Steps of Construction:
1. Draw a line segment DE = 5 cm.
2. At point E, construct a 90 degrees angle using a compass or set square, i.e., angle DEX = 90 degrees.
3. With E as center and radius 5 cm, draw an arc intersecting ray EX at point A. Join EA.
4. With A as center and radius 5 cm, draw an arc.
5. With D as center and radius 5 cm, draw another arc intersecting the previous arc at point R.
6. Join DR and AR.
DEAR is the required square.
In simple words: Draw the base side, make a 90 degrees corner at one end, mark equal sides of 5 cm all around, and join the vertices to form the square.

Exam Tip: All interior angles of a square are 90 degrees and all sides are equal, which simplifies construction using a protractor or compass.

Question 5. Construct a rectangle ABCD such that AB = 4 cm and diagonal BD is 5 cm.
Answer:
Steps of Construction:
1. Draw a line segment AB = 4 cm.
2. At point B, construct a 90 degrees angle, i.e., angle ABX = 90 degrees.
3. With A as center and radius equal to the diagonal BD = 5 cm, draw an arc intersecting ray BX at point D. (Since diagonals of a rectangle are equal, AC = BD = 5 cm, and in right triangle ABD, AD can also be found using Pythagoras theorem: \(AD = \sqrt{5^2 - 4^2} = 3\) cm).
4. Join AD and BD.
5. With D as center and radius 4 cm, draw an arc.
6. With A as center and radius equal to AD (3 cm), draw an arc intersecting at point C.
7. Join DC and BC.
ABCD is the required rectangle.
In simple words: Draw the base, erect a 90 degrees angle at one end, use the diagonal length to locate the opposite corner, and complete the rectangle using opposite side lengths.

Exam Tip: In a rectangle, adjacent sides meet at right angles, and opposite sides are equal in length.