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

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Question

Draw a rough figure of a quadrilateral that is not a parallelogram but hasexactly 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

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

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.