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If a Quadrilateral ABCD,∠A = 90∘ and AB = BC = CD = DA, Then ABCD is a
- a)Rectangle
- b)Parallelogram
- c)Square
- d)Triangle
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is ...
Step 1: Given that angle A = 90 degrees, we know that ABCD has one right angle.
Step 2: Since AB = BC = CD = DA, all sides of quadrilateral ABCD are equal in length. Let's denote the length of each side as 's'.
Step 3: Now, we have a quadrilateral with one right angle and all sides equal. This means that ABCD is an equilateral quadrilateral.
Step 4: In an equilateral quadrilateral with one right angle, the other angles must also be right angles. Therefore, angle B = angle C = angle D = 90 degrees.
Step 5: Since all angles are 90 degrees and all sides are equal, quadrilateral ABCD is a square.
Quadrilateral ABCD is a square.
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If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is ...
Understanding the Quadrilateral ABCD
In this problem, we have a quadrilateral ABCD with the following properties:
- ∠A = 90 degrees (a right angle)
- AB = BC = CD = DA (all sides are equal)
Identifying the Shape
Given the conditions, let's analyze the properties of quadrilateral ABCD:
- Since ∠A is a right angle, we know that the shape has one corner that is square.
- The equality of all sides (AB = BC = CD = DA) indicates that all sides are not only equal but also that the quadrilateral is regular.
Implications of Equal Sides
When a quadrilateral has all sides equal and one angle is a right angle, it leads us to a specific conclusion:
- The quadrilateral is symmetric and has equal length sides, which means it can only be a square.
- In a square, each angle measures 90 degrees, and all sides are equal, fulfilling both conditions given in the problem.
Conclusion
Thus, the quadrilateral ABCD, with its properties of one right angle and all sides of equal length, is confirmed to be a square.
Therefore, the correct answer is option 'C' - Square.
In this problem, we have a quadrilateral ABCD with the following properties:
- ∠A = 90 degrees (a right angle)
- AB = BC = CD = DA (all sides are equal)
Identifying the Shape
Given the conditions, let's analyze the properties of quadrilateral ABCD:
- Since ∠A is a right angle, we know that the shape has one corner that is square.
- The equality of all sides (AB = BC = CD = DA) indicates that all sides are not only equal but also that the quadrilateral is regular.
Implications of Equal Sides
When a quadrilateral has all sides equal and one angle is a right angle, it leads us to a specific conclusion:
- The quadrilateral is symmetric and has equal length sides, which means it can only be a square.
- In a square, each angle measures 90 degrees, and all sides are equal, fulfilling both conditions given in the problem.
Conclusion
Thus, the quadrilateral ABCD, with its properties of one right angle and all sides of equal length, is confirmed to be a square.
Therefore, the correct answer is option 'C' - Square.
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If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is aa)Rectangleb)Parallelogramc)Squared)TriangleCorrect answer is option 'C'. Can you explain this answer?
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If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is aa)Rectangleb)Parallelogramc)Squared)TriangleCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is aa)Rectangleb)Parallelogramc)Squared)TriangleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is aa)Rectangleb)Parallelogramc)Squared)TriangleCorrect answer is option 'C'. Can you explain this answer?.
If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is aa)Rectangleb)Parallelogramc)Squared)TriangleCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is aa)Rectangleb)Parallelogramc)Squared)TriangleCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a Quadrilateral ABCD,∠A= 90and AB = BC = CD = DA, Then ABCD is aa)Rectangleb)Parallelogramc)Squared)TriangleCorrect answer is option 'C'. Can you explain this answer?.
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