Notifications
Clear all
Circles
1
Posts
2
Users
0
Likes
309
Views
0
19/07/2021 12:59 pm
Topic starter
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
1 Answer
0
19/07/2021 1:06 pm
Construction:
Consider a trapezium ABCD with AB || CD and BC = AD
Draw AM CD and BN CD.
In △AMD and △BNC
The diagram will look as follows:
In △AMD and △BNC
AD = BC (Given)
AMD = BNC (By construction, each is 90°)
AM = BM (Perpendicular distance between two parallel lines is same)
△AMD △BNC (RHS Congruence rule)
ADC = BCD (CPCT) .....(1)
BAD and ADC are on the same side of transversal AD.
BAD + ADC = 180° .....(2)
BAD + BCD = 180° .....[using equation (1)]
This equation shows that the opposite angles are supplementary.
Therefore, ABCD is a cyclic quadrilateral.