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

In given figure AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD. Show that A>C and B>D.
463865.jpg

Open in App
Solution


ABCD is a quadrilateral such that AB is its smallest side and CD is its largest side.

Join AC and BD. Since AB is the smallest side of quadrilateral ABCD.

In ABC, we have

BC>AB

8>3 ... (1)
[Since angle opposite to longer side is greater]

Since CD is the longest side of quadrilateral ABCD.

Now, In ACD, we have

CD>AD

7>4 ... (2)
[Since angle opposite to longer side is greater]

Adding (1) and (2), we get

8+7>3+4

A>C

Again, in ABD, we have

AD>AB [Since AB is the shortest side]

1>6... (3)

In BCD, we have

CD>BC [Since CD is the longest side]

2>5 ... (4)

Adding (3) and (4), we get

1+2>5+6

B>D

Thus , A>C and B>D. [henceproved]

493581_463865_ans.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Ratio and Proportion
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon