Notifications
Clear all
Areas of Parallelograms and Triangles
1
Posts
2
Users
0
Likes
433
Views
0
16/07/2021 4:47 pm
Topic starter
ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (△ADX) = ar (△ACY).
1 Answer
0
16/07/2021 4:50 pm
Given,
ABCD is a trapezium with AB || DC.
XY || AC
Construction,
Join CX
To Prove:
ar(ADX) = ar(ACY)
Proof:
ar(△ADX) = ar(△AXC) — (i) (Since they are on the same base AX and in-between the same parallels AB and CD)
ar(△AXC)=ar(△ ACY) — (ii) (Since they are on the same base AC and in-between the same parallels XY and AC.)
(i) and (ii),
ar(△ADX) = ar(△ACY)