Guys even this is difficult for me
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Given: 1) ABCD is a trapezium.
2) AB // DC
3) AO / OC = BO / OD = 1 / 2
To find: DC
Solution: 1) In triangle AOB and triangle DOC,
AO / OC = BO / OD = 1 / 2 ... (Given)
2) Angle AOB = angle DOC ... (Vertically Opposite Angles)
3) Therefore,triangle AOB is similar to triangle DOC ... (SAS Similarity Test)
4) Thus, AB / DC =AO / OC = BO / OD = 1 / 2
Therefore, AB / DC = 1 / 2 i.e. 3 / DC = 1 / 2
Hence, DC = 6
2) AB // DC
3) AO / OC = BO / OD = 1 / 2
To find: DC
Solution: 1) In triangle AOB and triangle DOC,
AO / OC = BO / OD = 1 / 2 ... (Given)
2) Angle AOB = angle DOC ... (Vertically Opposite Angles)
3) Therefore,triangle AOB is similar to triangle DOC ... (SAS Similarity Test)
4) Thus, AB / DC =AO / OC = BO / OD = 1 / 2
Therefore, AB / DC = 1 / 2 i.e. 3 / DC = 1 / 2
Hence, DC = 6
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