Question

if one of the diagonals of a trapezium divides the other in the ratio of 2:1, prove that one of the parallel sides is 2 times the other.

Answer 1

Given : that diagonal BD divides diagonal AC in AO : OC with 3 : 1.

To prove : AB = 2 CD.

Proof : In triangle symbol AOC and triangle symbol DOC

∠AOB = ∠COD

∠OBA = ∠ODC ( because DC is parallel to AB and DB is the transversal, so these are alternate ∠s )

Therefore, triangle symbol AOB similar triangle symbol COD [ By AA Similarity ]

Now, AO / OC = AB / DC ( because in similar triangles sides are propotional )

2 / 1 = AB / DC ( given that AO : OC = 2 : 1 )

AB = 2 DC

hope it helps!!!!