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In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?
- a)An equilateral triangle.
- b)An isosceles but not a 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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Verified Answer
In a square ABCD, the diagonals bisect at O. What type of a triangle i...
Since diagonals of a square are equal and bisect at right angles, triangle AOB is an isosceles right angled triangle.
Most Upvoted Answer
In a square ABCD, the diagonals bisect at O. What type of a triangle i...
Solution:
Given: In a square ABCD, the diagonals bisect at O.
To find: What type of a triangle is AOB?
Explanation:
Let's draw the square ABCD and its diagonals as shown below:
https://www.edurev.in/api/img/content/d3da2fec9c2e0967d7b6a4f7a6b7e18f.png" />
From the above figure, we can see that:
- AO and BO are radii of the circle with center O.
- Since the diagonals of a square bisect each other, we have:
AO = BO = CO = DO
- Therefore, triangle AOB is an isosceles triangle with AB as the base and AO = BO as the equal sides.
Now, we need to determine if triangle AOB is also a right-angled triangle.
- Let's consider triangle AOD.
- In triangle AOD, we have:
AD = OD (as diagonals bisect each other)
angle AOD = 90 degrees (as diagonal BD is perpendicular to AD)
Therefore, triangle AOD is an isosceles right-angled triangle.
- Since AO = OD, we have:
angle ADO = angle AOD = 45 degrees
- Therefore, angle AOB = 2 x angle ADO = 2 x 45 = 90 degrees.
Hence, we can conclude that triangle AOB is an isosceles right-angled triangle.
Therefore, the correct answer is option (D) - An isosceles right-angled triangle.
Given: In a square ABCD, the diagonals bisect at O.
To find: What type of a triangle is AOB?
Explanation:
Let's draw the square ABCD and its diagonals as shown below:
From the above figure, we can see that:
- AO and BO are radii of the circle with center O.
- Since the diagonals of a square bisect each other, we have:
AO = BO = CO = DO
- Therefore, triangle AOB is an isosceles triangle with AB as the base and AO = BO as the equal sides.
Now, we need to determine if triangle AOB is also a right-angled triangle.
- Let's consider triangle AOD.
- In triangle AOD, we have:
AD = OD (as diagonals bisect each other)
angle AOD = 90 degrees (as diagonal BD is perpendicular to AD)
Therefore, triangle AOD is an isosceles right-angled triangle.
- Since AO = OD, we have:
angle ADO = angle AOD = 45 degrees
- Therefore, angle AOB = 2 x angle ADO = 2 x 45 = 90 degrees.
Hence, we can conclude that triangle AOB is an isosceles right-angled triangle.
Therefore, the correct answer is option (D) - An isosceles right-angled triangle.
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In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?a)An equilateral triangle.b)An isosceles but not a 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, the diagonals bisect at O. What type of a triangle is AOB?a)An equilateral triangle.b)An isosceles but not a 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? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?a)An equilateral triangle.b)An isosceles but not a 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? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?a)An equilateral triangle.b)An isosceles but not a 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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