. If one diagonal of a trapezium divides the other diagonal in the ratio 2:1.prove that one of its parallel sides is twice the other?
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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
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
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