Excercise 4.4 Practical Geometry- NCERT Solutions Class 8
Practical Geometry
Chapter 4 Ex.4.4 Question 1
Construct the following quadrilaterals.
(i) Quadrilateral \(DEAR\)
\(DE = 4\,\rm{cm}\)
\(EA = 5\,\rm{cm}\)
\(AR = 4.5\,\rm{cm}\)
\(\angle E = 60^\circ\)
\(\angle A = 90^\circ\)
(ii) Quadrilateral \(TRUE\)
\(TR = 3.5\,\rm{cm}\)
\(RU = 3\,\rm{cm }\)
\(UE = 4\,\rm{cm}\)
\(\angle R = 75^\circ\)
\(\angle U=120^\circ\)
Solution

What is known?
Measurements of a Quadrilateral (\(3\) line segments and \(2\) angles).
What is unknown?
Construction of a Quadrilateral
Reasoning:
As you are aware, we need five measurements to draw a quadrilateral. The given measurements are of three sides and two included angles (Page 58 of Grade 8 NCERT Book)
Steps:
Let us draw a rough diagram with the given measurements to find out whether it is possible to construct a quadrilateral
Let us construct the quadrilateral
Step 1: Draw a line segment \(TR = 3.5\,\rm{cm.}\)
Step 2: With \(R\) as center construct an angle of \(75^\circ.\) With \(R\) as center and radius \(3\,\rm{cm}\) draw an arc cutting the ray from \(R\) at \(U.\)
Step 3: With \(U\) as center construct an angle of \(120^\circ.\) With \(U\) as center and radius \(4\,\rm{cm}\) draw an arc cutting the ray from \(U\) at \(E.\)
Step 4: Join \(TE.\)
Step 5: \(TRUE\) is the required quadrilateral.