CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the adjoining figure, ABCD is a parallelogram and X, Y are the points on diagonal BD, such that DX = BY. Prove that CXAY is a parallelogram.

Open in App
Solution



Given : ABCD is a parallelogram.
To prove: CXAY is a parallelogram.
Construction : Join AC, meeting BD at O.
Proof: We know that the diagonals of a parallelogram bisect each other.
So, OA = OC and OD = OB.
OD = OB...(i)
DX = BY.........(ii)
Subtracting (ii) from (i),we get:
OD-DX = OB-BY
OX = OY

Since, CXAY is a quadrilateral whose diagonals bisect each other, it is a parallelogram.

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Parallelograms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon