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In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?
- a)A square
- b)A parallelogram
- c)A rhombus
- d)A trapezium
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In the quadrilateral ABCD, the diagonals AC and BD are equal and perpe...
A quadrilateral in which the diagonals are equal and perpendicular is called a square.
Most Upvoted Answer
In the quadrilateral ABCD, the diagonals AC and BD are equal and perpe...
**Given Information:**
- In quadrilateral ABCD, the diagonals AC and BD are equal in length.
- The diagonals AC and BD are perpendicular to each other.
**Definition of a Square:**
- A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees.
**Explanation:**
To determine the type of quadrilateral ABCD, we need to analyze the given information.
1. **Equal Diagonals:** The diagonals AC and BD are equal in length. This property is common to several types of quadrilaterals, including squares, rhombuses, and parallelograms.
2. **Perpendicular Diagonals:** The diagonals AC and BD are perpendicular to each other. This property eliminates the possibility of the quadrilateral being a rhombus or a parallelogram because these quadrilaterals do not have perpendicular diagonals.
3. **Conclusion:** The given information satisfies the properties of a square - a quadrilateral with equal diagonals that are perpendicular to each other. Therefore, the quadrilateral ABCD must be a square.
**Answer:**
The quadrilateral ABCD is a square (option A).
- In quadrilateral ABCD, the diagonals AC and BD are equal in length.
- The diagonals AC and BD are perpendicular to each other.
**Definition of a Square:**
- A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees.
**Explanation:**
To determine the type of quadrilateral ABCD, we need to analyze the given information.
1. **Equal Diagonals:** The diagonals AC and BD are equal in length. This property is common to several types of quadrilaterals, including squares, rhombuses, and parallelograms.
2. **Perpendicular Diagonals:** The diagonals AC and BD are perpendicular to each other. This property eliminates the possibility of the quadrilateral being a rhombus or a parallelogram because these quadrilaterals do not have perpendicular diagonals.
3. **Conclusion:** The given information satisfies the properties of a square - a quadrilateral with equal diagonals that are perpendicular to each other. Therefore, the quadrilateral ABCD must be a square.
**Answer:**
The quadrilateral ABCD is a square (option A).
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In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?a)A squareb)A parallelogramc)A rhombusd)A trapeziumCorrect answer is option 'A'. Can you explain this answer?
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