GSEB Class 8 Maths Solutions Chapter 4 Practical Geometry Exercise 4.4

Question 1. Construct the following quadrilaterals.
(i) Quadrilateral DEAR
DE = 4 cm
EA = 5 cm
AR = 4.5 cm
\( \angle E = 60^\circ \)
\( \angle A = 90^\circ \)
(ii) Quadrilateral TRUE
TR = 3.5 cm
RU = 3 cm
UE = 4 cm
\( \angle U = 120^\circ \)

Answer:
(i) Steps of construction:
I. First, draw a line segment DE that is 4 cm long.
II. At point E, draw a ray \( \overrightarrow { EX } \) so that \( \angle DEX \) measures \( 60^\circ \).
III. From the ray \( \overrightarrow { EX } \), cut off a segment EA that is 5 cm long.
IV. At point A, draw a ray \( \overrightarrow {AY } \) such that \( \angle EAY \) is \( 90^\circ \).
V. From the ray \( \overrightarrow { AY } \), cut off a segment AR that is 4.5 cm long.
VI. Then, join points R and D.
Thus, DEAR is the required quadrilateral.

Exam Tip: When constructing a quadrilateral with two given angles, ensure you draw the angles correctly using a protractor at the specified vertices and extend rays for the corresponding side lengths.

(ii) Steps of construction:
I. First, draw a line segment TR that is 3.5 cm long.
II. At point R, draw a ray \( \overrightarrow { RX } \) so that \( \angle TRX \) measures \( 75^\circ \).
III. From the ray \( \overrightarrow { RX } \), cut off a segment RU that is 3 cm long.
IV. At point U, draw a ray \( \overrightarrow { UY } \) such that \( \angle RUY \) measures \( 120^\circ \).
V. From the ray UY, cut off a segment UE that is 4 cm long.
VI. Then, join points E and T.
Thus, TRUE is the required quadrilateral.

Exam Tip: Always make sure your construction lines are light and clear, and your final quadrilateral is drawn with darker lines to distinguish it from the construction steps.