## 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 \(TRUE\)

\(TR = 3.5\,\rm{cm}\)

\(RU = 3\,\rm{cm }\)

\(UE = 4\,\rm{cm}\)

\(\angle R = 75^\circ\)

\(\angle U=120^\circ\)

**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.