Question

diagonals SA and TR of quadi STAR intersect at O in such a way that SOR=TOA.prove that STAR is a trapezium.

Answer 1

Construct:-OM|| AR ----------------- 1
Proof :- By BPT
OM|| AR
SM/ MR = SO/OR ------------------------ (I)
In ∆ SOR &∆ TOA
since they are equal .
Therefore -- SO/OR = OT/ OA ----------------- (ii)
From (i) and (ii)
SM/MR= OT/ OA
But OA = OR
Therefore
SM/MR=OT/OR
THEREFORE
OM|ST --------------- 2
FROM 1 AND 2
AR || ST
Since opposite sides of quadrilateral are parallel
:. STAR is a trapezium.