What is the definition of an irregular quadrilateral?

Answer

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Hint: We clear the concept of regular quadrilateral and then using the opposite concept we get irregular quadrilateral. We use the example and the image of an irregular quadrilateral to understand the concept better.

Complete step by step solution:

To understand irregular quadrilaterals, we first understand the concept of regular quadrilaterals. Quadrilaterals like squares which have congruent sides and angles being equal to each other can be called a regular quadrilateral.

The image of regular quadrilateral will be

Now the opposite concept where quadrilaterals like rectangle, rhombus which don’t have congruent sides or angles being equal to each other can be called as irregular quadrilateral.

A polygon having four sides, but all four (opposite) sides and angles are incongruent can also be called irregular quadrilateral.

For the below image we can see that the consecutive angles are not similar to each other. The angles are ${{98.6}^{\circ }},{{97}^{\circ }},{{51.5}^{\circ }},{{113}^{\circ }}$.

The length of the sides is also unequal to each other.

They are $5.8,3.3,7.8,8.5$.

Therefore, this quadrilateral is an irregular quadrilateral.

Note: We can’t confuse between being congruent and regular. There is no such quadrilateral that has four congruent sides but is irregular because the only quadrilateral that has four congruent sides is a square, which is a regular quadrilateral.

Complete step by step solution:

To understand irregular quadrilaterals, we first understand the concept of regular quadrilaterals. Quadrilaterals like squares which have congruent sides and angles being equal to each other can be called a regular quadrilateral.

The image of regular quadrilateral will be

Now the opposite concept where quadrilaterals like rectangle, rhombus which don’t have congruent sides or angles being equal to each other can be called as irregular quadrilateral.

A polygon having four sides, but all four (opposite) sides and angles are incongruent can also be called irregular quadrilateral.

For the below image we can see that the consecutive angles are not similar to each other. The angles are ${{98.6}^{\circ }},{{97}^{\circ }},{{51.5}^{\circ }},{{113}^{\circ }}$.

The length of the sides is also unequal to each other.

They are $5.8,3.3,7.8,8.5$.

Therefore, this quadrilateral is an irregular quadrilateral.

Note: We can’t confuse between being congruent and regular. There is no such quadrilateral that has four congruent sides but is irregular because the only quadrilateral that has four congruent sides is a square, which is a regular quadrilateral.

Last updated date: 23rd Aug 2023

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