UPSC Exam  >  UPSC Questions  >  Rhombus is a quadrilaterala)in which diagonal... Start Learning for Free
Rhombus is a quadrilateral
  • a)
    in which diagonals are at right angle
  • b)
    in which diagonals are inclines at an angle of 60
  • c)
    in which diagonals bisect each other
  • d)
    in which diagonals bisect opposite angles
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Rhombus is a quadrilaterala)in which diagonals are at right angleb)in ...
This is because in a rhombus, the diagonals always bisect each other at right angles (90 degrees). While the diagonals do bisect each other (option C) and also bisect the opposite angles (option D), the defining characteristic in the context of a rhombus's diagonal properties is that they are perpendicular.
So, if the question specifically asks about the nature of the diagonals' intersection, option A is the most accurate. Option D, "in which diagonals bisect opposite angles," is also true but is not specifically about the angle at which they bisect each other.
Free Test
Community Answer
Rhombus is a quadrilaterala)in which diagonals are at right angleb)in ...
A rhombus is a quadrilateral with certain unique properties. The correct answer is option 'D', which states that a rhombus is a quadrilateral in which the diagonals bisect opposite angles. Let's understand why this is the correct answer.

Diagonals of a Rhombus:
- A rhombus has two pairs of opposite sides that are equal in length.
- The diagonals of a rhombus are the line segments connecting opposite vertices.

Bisecting Opposite Angles:
- When we say that the diagonals of a rhombus bisect opposite angles, it means that the diagonals divide the rhombus into four congruent triangles.
- Each diagonal cuts the rhombus into two equal parts, and these parts are congruent.
- As a result, the opposite angles formed by the diagonals are equal in measure.

Proof of Diagonal Bisecting Opposite Angles:
To prove that the diagonals of a rhombus bisect opposite angles, we can use the concept of congruent triangles.
Let's consider a rhombus ABCD with diagonals AC and BD.

Proof:
1. In rhombus ABCD, opposite sides are equal. Therefore, AB = BC = CD = DA.
2. Diagonals of a rhombus bisect each other. Therefore, AC and BD intersect at point O such that AO = OC and BO = OD.
3. Now, consider triangle ABO and triangle BCO.
- AB = BC (opposite sides of the rhombus)
- AO = OC (diagonals bisect each other)
- BO = BO (common side)
By side-side-side congruence, we can conclude that triangle ABO is congruent to triangle BCO.
4. Congruent triangles have equal corresponding angles. Therefore, angle AOB = angle BOC.
5. Similarly, we can prove that angle COD = angle DOA.
6. Hence, the diagonals of a rhombus bisect opposite angles.

Conclusion:
Based on the properties of a rhombus and the proof provided, it is clear that option 'D' is the correct answer. A rhombus is a quadrilateral in which the diagonals bisect opposite angles.
Explore Courses for UPSC exam

Top Courses for UPSC

Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer?
Question Description
Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. 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 Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC. Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Rhombus is a quadrilaterala)in which diagonals are at right angleb)in which diagonals are inclines at an angle of 60c)in which diagonals bisect each otherd)in which diagonals bisect opposite anglesCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice UPSC tests.
Explore Courses for UPSC exam

Top Courses for UPSC

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev