# Ex.3.3 Q4 Understanding Quadrilaterals Solution-Ncert Maths Class 8

## Question

Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

## Text Solution

**What is Known?**

Draw a figure of quadrilateral having two opposite angles of equal measure.

**What is Unknown?**

\(ABCD\) is quadrilateral whose opposite angles are equal.

**Reasoning:**

The opposite angles of a parallelogram are equal.

**Steps:**

In a kite, the angle between unequal sides are equal.

Draw line from \(A\) to \(C\) and we will get two triangles with common base \(AC\).

In \(∆ABC\) and \(∆ADC \) we have,

\({\rm{AB}} = {\rm{ AD }},{\rm{ BC}} = {\rm{CD}}\) ; \(AC\) is common to both

\(\Delta {\rm{ABC }}\!\!\cong\!\!\Delta {\rm{ADC }}\text{[congruent triangles]}\)

Hence corresponding parts of congruent triangles are equal.

Therefore\(\angle {\rm{B}} = \angle {\rm{D}}\)

However, the quadrilateral \(ABCD\) is not a parallelogram as the measures of the remaining pair of opposite angles, \(\angle {\rm{A}}\) and \(\angle {\rm{C}}\), are not equal. Since they form angle between equal sides.