Class 9 Exam > Class 9 Questions > In a Quadrilateral ABCD, AB = BC and CD = DA,...
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In a Quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral is a
- a)Triangle
- b)Kite
- c)Rhombus
- d)Rectangle
Correct answer is option 'B'. Can you explain this answer?
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In a Quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral i...
Given:
In a quadrilateral ABCD, AB = BC and CD = DA
To find:
The type of quadrilateral ABCD
Solution:
To determine the type of quadrilateral ABCD, we need to analyze the given conditions.
1. AB = BC:
This condition implies that side AB is equal in length to side BC. This means that AB and BC are adjacent sides of the quadrilateral.
2. CD = DA:
This condition implies that side CD is equal in length to side DA. This means that CD and DA are also adjacent sides of the quadrilateral.
Analysis:
Based on the given conditions, we can conclude the following:
- The opposite sides AB and CD are not equal in length.
- The opposite sides BC and DA are not equal in length.
- The adjacent sides AB and BC are equal in length.
- The adjacent sides CD and DA are equal in length.
From these observations, we can determine that the quadrilateral ABCD is a kite.
Definition of a Kite:
A kite is a quadrilateral with two pairs of adjacent sides that are congruent. In a kite, the diagonals are perpendicular to each other and the longer diagonal bisects the shorter diagonal.
Explanation:
In the given quadrilateral ABCD, the sides AB and BC are equal in length, and the sides CD and DA are equal in length. This satisfies the condition of a kite where two pairs of adjacent sides are congruent.
Hence, the quadrilateral ABCD is a kite.
In a quadrilateral ABCD, AB = BC and CD = DA
To find:
The type of quadrilateral ABCD
Solution:
To determine the type of quadrilateral ABCD, we need to analyze the given conditions.
1. AB = BC:
This condition implies that side AB is equal in length to side BC. This means that AB and BC are adjacent sides of the quadrilateral.
2. CD = DA:
This condition implies that side CD is equal in length to side DA. This means that CD and DA are also adjacent sides of the quadrilateral.
Analysis:
Based on the given conditions, we can conclude the following:
- The opposite sides AB and CD are not equal in length.
- The opposite sides BC and DA are not equal in length.
- The adjacent sides AB and BC are equal in length.
- The adjacent sides CD and DA are equal in length.
From these observations, we can determine that the quadrilateral ABCD is a kite.
Definition of a Kite:
A kite is a quadrilateral with two pairs of adjacent sides that are congruent. In a kite, the diagonals are perpendicular to each other and the longer diagonal bisects the shorter diagonal.
Explanation:
In the given quadrilateral ABCD, the sides AB and BC are equal in length, and the sides CD and DA are equal in length. This satisfies the condition of a kite where two pairs of adjacent sides are congruent.
Hence, the quadrilateral ABCD is a kite.
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Community Answer
In a Quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral i...
In kite every side is equal and in square as well but there is no square in option so kite is the right answer.
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In a Quadrilateral ABCD, AB = BC and CD = DA, then the quadrilateral is aa)Triangleb)Kitec)Rhombusd)RectangleCorrect answer is option 'B'. Can you explain this answer?
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