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ABCD is a ||gm and X, Y are the mid - points of sides AB and CD respectively, then
- a)AXCY is rectangle
- b)AXCY is square
- c)AXCY is parallelogram
- d)AXCY is rhombus.
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
ABCD is a ||gm and X, Y are the mid - points of sides AB and CD respec...
And also,
AB || CD, or AX || CY
∵ AX = CY and AX || CY
∴ AXCY is a ||gm
(∴ one pair of sides are equal and parallel)
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ABCD is a ||gm and X, Y are the mid - points of sides AB and CD respec...
Understanding the Quadrilateral ABCD
ABCD is a parallelogram, which means opposite sides are equal and parallel. Let's analyze the implications for the midpoints X and Y.
Midpoints X and Y
- X is the midpoint of side AB.
- Y is the midpoint of side CD.
Connecting the Midpoints
When we connect points X and Y, we create line segment XY. In a parallelogram, the line segment joining the midpoints of two sides is parallel to the other pair of sides and half as long.
Characteristics of AXCY
- Parallelogram: The segments AX and CY are equal in length (since X and Y are midpoints) and parallel (as they are formed from the same sides of the parallelogram).
- Opposite Sides: AX is parallel and equal to CY, and AC is parallel and equal to XY. This confirms that AXCY is a parallelogram.
Conclusion
Since AXCY has both pairs of opposite sides that are equal and parallel, it meets the definition of a parallelogram. Thus, the correct answer is option 'C' that states AXCY is a parallelogram.
In summary, the properties of midpoints in a parallelogram lead us to the conclusion that the figure formed by connecting these midpoints will always be a parallelogram, reinforcing the geometric principles at play.
ABCD is a parallelogram, which means opposite sides are equal and parallel. Let's analyze the implications for the midpoints X and Y.
Midpoints X and Y
- X is the midpoint of side AB.
- Y is the midpoint of side CD.
Connecting the Midpoints
When we connect points X and Y, we create line segment XY. In a parallelogram, the line segment joining the midpoints of two sides is parallel to the other pair of sides and half as long.
Characteristics of AXCY
- Parallelogram: The segments AX and CY are equal in length (since X and Y are midpoints) and parallel (as they are formed from the same sides of the parallelogram).
- Opposite Sides: AX is parallel and equal to CY, and AC is parallel and equal to XY. This confirms that AXCY is a parallelogram.
Conclusion
Since AXCY has both pairs of opposite sides that are equal and parallel, it meets the definition of a parallelogram. Thus, the correct answer is option 'C' that states AXCY is a parallelogram.
In summary, the properties of midpoints in a parallelogram lead us to the conclusion that the figure formed by connecting these midpoints will always be a parallelogram, reinforcing the geometric principles at play.
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ABCD is a ||gm and X, Y are the mid - points of sides AB and CD respectively, thena)AXCY is rectangleb)AXCY is squarec)AXCY is parallelogramd)AXCY is rhombus.Correct answer is option 'C'. Can you explain this answer?
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ABCD is a ||gm and X, Y are the mid - points of sides AB and CD respectively, thena)AXCY is rectangleb)AXCY is squarec)AXCY is parallelogramd)AXCY is rhombus.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for ABCD is a ||gm and X, Y are the mid - points of sides AB and CD respectively, thena)AXCY is rectangleb)AXCY is squarec)AXCY is parallelogramd)AXCY is rhombus.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of ABCD is a ||gm and X, Y are the mid - points of sides AB and CD respectively, thena)AXCY is rectangleb)AXCY is squarec)AXCY is parallelogramd)AXCY is rhombus.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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