GSEB Class 8 Maths Solutions Chapter 4 Practical Geometry Exercise 4.3

Question 1. Construct the following quadrilaterals:
(i) Quadrilateral MORE
MO = 6 cm
OR = 4.5 cm
\( \angle M = 60^\circ \)
\( \angle O = 105^\circ \)
\( \angle R = 105^\circ \)
Answer:
(i) Steps for building:
I. First, draw a line segment MO measuring 6 cm.
II. Next, at point M, draw a ray \( \overrightarrow { MX } \) so that the angle \( \angle OMX \) measures \( 60^\circ \).
III. Then, at point O, draw another ray \( \overrightarrow { OY} \) such that angle \( \angle MOY \) is \( 105^\circ \).
IV. From ray \( \overrightarrow { OY } \), measure and cut off a segment OR which is 4.5 cm long.
V. After that, at point R, draw ray \( \overrightarrow { RZ } \) such that angle \( \angle ORZ \) equals \( 105^\circ \).
Let the ray \( \overrightarrow { RZ } \) cross ray \( \overrightarrow {MX} \) at point E.
Therefore, MORE is the desired quadrilateral.
In simple words: To construct this quadrilateral, you follow steps to draw a base line, then draw specific angles and lengths from each end, until all points are connected to form the shape.

Exam Tip: Ensure your protractor and ruler are used accurately for precise angle and length measurements, as small errors can affect the final figure.

Question 1. Construct the following quadrilaterals:
(ii) Quadrilateral PLAN
PL = 4 cm
LA = 6.5 cm
\( \angle P = 90^\circ \)
\( \angle N = 85^\circ \)
Answer:
(ii) Steps for building:
I. First, draw a line segment AL that is 6.5 cm long.
II. Next, at point A, draw a ray \( \overrightarrow { AX } \) so that angle \( \angle LAX \) measures \( 110^\circ \).
III. Then, at point L, draw another ray \( \overrightarrow { LY } \) such that angle \( \angle ALY \) is \( 75^\circ \).
Keep in mind: The angle \( \angle L = 75^\circ \) was not directly given, but we can find it using the angle sum property of quadrilaterals.
The total of the three known angles is \( 110^\circ + 90^\circ + 85^\circ = 285^\circ \).
So, the fourth angle \( \angle L \) is \( 360^\circ - 285^\circ = 75^\circ \).
IV. From ray \( \overrightarrow { LY } \), measure and cut off a segment LP that is 4 cm long.
V. After that, at point P, draw a ray \( \overrightarrow { PZ } \) so that angle \( \angle LPZ \) measures \( 90^\circ \).
Let ray \( \overrightarrow { PZ } \) and ray \( \overrightarrow { AX } \) meet at point N.
Therefore, PLAN is the desired quadrilateral.
In simple words: Start by drawing a base line, then measure and draw angles and segment lengths from the known points. Remember to calculate any missing angles using the total angle sum for the shape.

Exam Tip: Always calculate any missing angles using properties of the shape (like angle sum of a quadrilateral being \( 360^\circ \)) before starting the construction, to ensure you have all necessary information.

Question 1. Construct the following quadrilaterals:
(iii) Parallelogram HEAR
HE = 5 cm
EA = 6 cm
\( \angle E = 85^\circ \)
Answer:
(iii) Steps for building:
I. First, make a line segment HE that is 5 cm long.
II. Next, at point E, draw a ray \( \overrightarrow { EX } \) so that angle \( \angle HEA \) measures \( 85^\circ \).
III. Then, from ray \( \overrightarrow { EX } \), mark off a segment EA with a length of 6 cm.
IV. After that, with A as the center and a radius of 5 cm, draw an arc towards point H.
V. Also, with H as the center and a radius of 6 cm, draw another arc that crosses the first arc at point R.
VI. Finally, connect points R and A, and R and H.
In this way, HEAR becomes the desired parallelogram.
In simple words: To build a parallelogram, draw one side and an angle, then mark off the adjacent side's length. Use compass arcs from two points to find the fourth point, completing the shape.

Exam Tip: For parallelograms, remember that opposite sides are equal in length and opposite angles are equal, which can help in cross-checking your construction.

Question 1. Construct the following quadrilaterals:
(iv) Rectangle OKAY
OK = 7 cm
KA = 5 cm
Answer:
(iv) Steps for building:
I. First, draw a line segment OK that is 7 cm long.
II. Next, at point O, draw a ray \( \overrightarrow { OP } \) so that angle \( \angle KOP \) measures \( 90^\circ \).
III. Then, from ray \( \overrightarrow { OP} \), measure and mark off a segment OY of 5 cm.
IV. After that, at point K, draw a ray \( \overrightarrow { KQ } \) such that angle \( \angle OKQ \) is \( 90^\circ \).
V. From ray \( \overrightarrow { KQ } \), measure and cut off a segment KA which is 5 cm long.
VI. Finally, connect points A and Y.
Therefore, OKAY is the desired rectangle.
In simple words: Constructing a rectangle involves drawing a base, then drawing perpendicular lines (90-degree angles) from its ends, and marking off the height to complete the shape.

Exam Tip: Always use a set square or protractor to ensure the \( 90^\circ \) angles are perfectly accurate, as this is crucial for constructing a rectangle.