GSEB Class 8 Maths Solutions Chapter 4 Practical Geometry Exercise 4.1

Question 1. Construct the following quadrilaterals.
(i) Quadrilateral ABCD
\( \text{AB} = 4.5 \text{ cm} \)
\( \text{BC} = 5.5 \text{ cm} \)
\( \text{CD} = 4 \text{ cm} \)
\( \text{AD} = 6 \text{ cm} \)
\( \text{AC} = 7 \text{ cm} \)
(ii) Quadrilateral JUMP
\( \text{JU} = 3.5 \text{ cm} \)
\( \text{UM} = 4 \text{ cm} \)
\( \text{MP} = 5 \text{ cm} \)
\( \text{PJ} = 4.5 \text{ cm} \)
\( \text{PU} = 6.5 \text{ cm} \)
(iii) Parallelogram MORE
\( \text{OR} = 6 \text{ cm} \)
\( \text{BE} = 4.5 \text{ cm} \)
\( \text{RE} = 4.5 \text{ cm} \)
\( \text{ET} = 6 \text{ cm} \)
\( \text{EO} = 7.5 \text{ cm} \)
(iv) Rhombus BEST
\( \text{BE} = 4.5 \text{ cm} \)
\( \text{ET} = 6 \text{ cm} \)
Answer: Before making a detailed construction for each of the given quadrilaterals, it is important to draw a rough sketch and mark all the provided measurements on it.

(i) Steps of construction for Quadrilateral ABCD:
I. Start by drawing a line segment \( \text{AB} = 4.5 \text{ cm} \).
II. With point \( \text{A} \) as the center and a radius of \( 7 \text{ cm} \), draw an arc.
III. Then, with point \( \text{B} \) as the center and a radius of \( 5.5 \text{ cm} \), draw another arc to make it cross the previous arc at point \( \text{C} \).
IV. Using point \( \text{A} \) as the center and a radius of \( 6 \text{ cm} \), draw an arc on the side opposite to where point \( \text{B} \) is.
V. Next, with point \( \text{C} \) as the center and a radius of \( 4 \text{ cm} \), draw another arc to make it cross the earlier arc at point \( \text{D} \).
VI. Finally, join the points \( \text{A} \) to \( \text{C} \), \( \text{B} \) to \( \text{C} \), \( \text{D} \) to \( \text{A} \) and \( \text{D} \) to \( \text{C} \). This forms \( \text{ABCD} \), the desired quadrilateral.

(ii) Steps of construction for Quadrilateral JUMP:
I. Begin by drawing a line segment \( \text{JU} = 3.5 \text{ cm} \).
II. With point \( \text{U} \) as the center and a radius of \( 6.5 \text{ cm} \), draw an arc.
III. Then, with point \( \text{J} \) as the center and a radius of \( 4.5 \text{ cm} \), draw another arc to make it cross the previous arc at point \( \text{P} \).
IV. Using point \( \text{U} \) as the center and a radius of \( 4 \text{ cm} \), draw an arc on the side opposite to where point \( \text{J} \) is.
V. Next, with point \( \text{P} \) as the center and a radius of \( 4 \text{ cm} \), draw another arc, making it intersect the earlier arc at point \( \text{M} \).
VI. Finally, join the points \( \text{P} \) to \( \text{J} \), \( \text{P} \) to \( \text{U} \), \( \text{P} \) to \( \text{M} \) and \( \text{U} \) to \( \text{M} \). This creates \( \text{JUMP} \), the desired quadrilateral.

(iii) Steps of construction for Parallelogram MORE:
I. First, draw a line segment \( \text{ER} = 4.5 \text{ cm} \).
II. With point \( \text{E} \) as the center and a radius of \( 7.5 \text{ cm} \), draw an arc.
III. Then, with point \( \text{R} \) as the center and a radius of \( 6 \text{ cm} \), draw another arc to make it cross the earlier arc at point \( \text{O} \).
IV. Using point \( \text{R} \) as the center and a radius of \( 6 \text{ cm} \), draw an arc on the side opposite to point \( \text{R} \).
V. Next, with point \( \text{O} \) as the center and a radius of \( 4.5 \text{ cm} \), draw another arc to make it intersect the previous arc at point \( \text{M} \).
VI. Finally, join the points \( \text{R} \) to \( \text{O} \), \( \text{E} \) to \( \text{M} \), \( \text{E} \) to \( \text{O} \) and \( \text{M} \) to \( \text{O} \). So, \( \text{EROM} \) or \( \text{MORE} \) is the desired parallelogram.

(iv) Steps of construction for Rhombus BEST:
I. Start by drawing a line segment \( \text{BE} = 4.5 \text{ cm} \).
II. With point \( \text{E} \) as the center and a radius of \( 6 \text{ cm} \), draw an arc.
III. Then, with point \( \text{B} \) as the center and a radius of \( 4.5 \text{ cm} \), draw another arc to make it cross the previous arc at point \( \text{T} \).
IV. Join points \( \text{T} \) to \( \text{B} \) and \( \text{T} \) to \( \text{E} \).
V. Using point \( \text{T} \) as the center and a radius of \( 4.5 \text{ cm} \), draw an arc on the side opposite to where point \( \text{B} \) is.
VI. Next, with point \( \text{E} \) as the center and a radius of \( 4.5 \text{ cm} \), draw another arc to make it intersect the previous arc at point \( \text{S} \).
VII. Finally, join points \( \text{S} \) to \( \text{T} \) and \( \text{S} \) to \( \text{E} \). Therefore, \( \text{BEST} \) is the desired rhombus. All four sides of a rhombus are equal in length.
In simple words: To build these shapes, first sketch them roughly and label all the given side lengths and diagonal lengths. Then, follow the step-by-step instructions using a ruler and compass to draw the actual figure. For a rhombus, remember that all its sides have the same length.

Exam Tip: Always begin construction by drawing a rough sketch with all given measurements, as this helps visualize the final figure and plan the steps accurately. Additionally, remember the properties of special quadrilaterals, like a rhombus having all sides equal, as this can simplify the construction process.