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In a square ABCD, its diagonals bisect at O. Then the triangle AOB is
- a)An equilateral triangle
- b)An isosceles but not right angled triangle
- c)A right angled but not an isosceles triangle
- d)An isosceles right angled triangle
Correct answer is option 'D'. Can you explain this answer?
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In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa...
Given:
Square ABCD with diagonals AC and BD that intersect at point O.
To find:
The type of triangle AOB.
Solution:
1. Properties of a Square:
- All sides of a square are equal in length.
- Opposite sides of a square are parallel.
- Diagonals of a square bisect each other at right angles.
2. Analyzing Triangle AOB:
- Triangle AOB is formed by connecting points A, O, and B.
- Since AOB is a triangle within a square, we can conclude that AO and BO are equal in length.
- The reason for this is that all sides of a square are equal in length.
- Therefore, triangle AOB is an isosceles triangle.
3. Diagonals of a Square:
- The diagonals of a square bisect each other at right angles.
- Since AC and BD are diagonals of the square ABCD, they bisect each other at right angles at point O.
4. Consequence of Bisecting Diagonals:
- When diagonals bisect each other at right angles, the resulting triangles are right-angled triangles.
- Therefore, triangle AOB is a right-angled triangle.
5. Conclusion:
- From our analysis, we can conclude that triangle AOB is an isosceles right-angled triangle.
Answer:
- The correct answer is option 'D': An isosceles right-angled triangle.
Square ABCD with diagonals AC and BD that intersect at point O.
To find:
The type of triangle AOB.
Solution:
1. Properties of a Square:
- All sides of a square are equal in length.
- Opposite sides of a square are parallel.
- Diagonals of a square bisect each other at right angles.
2. Analyzing Triangle AOB:
- Triangle AOB is formed by connecting points A, O, and B.
- Since AOB is a triangle within a square, we can conclude that AO and BO are equal in length.
- The reason for this is that all sides of a square are equal in length.
- Therefore, triangle AOB is an isosceles triangle.
3. Diagonals of a Square:
- The diagonals of a square bisect each other at right angles.
- Since AC and BD are diagonals of the square ABCD, they bisect each other at right angles at point O.
4. Consequence of Bisecting Diagonals:
- When diagonals bisect each other at right angles, the resulting triangles are right-angled triangles.
- Therefore, triangle AOB is a right-angled triangle.
5. Conclusion:
- From our analysis, we can conclude that triangle AOB is an isosceles right-angled triangle.
Answer:
- The correct answer is option 'D': An isosceles right-angled triangle.
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In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa)An equilateral triangleb)An isosceles but not right angled trianglec)A right angled but not an isosceles triangled)An isosceles right angled triangleCorrect answer is option 'D'. Can you explain this answer?
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In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa)An equilateral triangleb)An isosceles but not right angled trianglec)A right angled but not an isosceles triangled)An isosceles right angled triangleCorrect answer is option 'D'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa)An equilateral triangleb)An isosceles but not right angled trianglec)A right angled but not an isosceles triangled)An isosceles right angled triangleCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa)An equilateral triangleb)An isosceles but not right angled trianglec)A right angled but not an isosceles triangled)An isosceles right angled triangleCorrect answer is option 'D'. Can you explain this answer?.
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In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa)An equilateral triangleb)An isosceles but not right angled trianglec)A right angled but not an isosceles triangled)An isosceles right angled triangleCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa)An equilateral triangleb)An isosceles but not right angled trianglec)A right angled but not an isosceles triangled)An isosceles right angled triangleCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of In a square ABCD, its diagonals bisect at O. Then the triangle AOB isa)An equilateral triangleb)An isosceles but not right angled trianglec)A right angled but not an isosceles triangled)An isosceles right angled triangleCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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