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Class 10 > Learn Mathematics > If one diagonal of a trapezium divides the other diagonal...
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If one diagonal of a trapezium divides the other diagonal in the ratio 1:3. Prove that one of the parallel sides is three times the other.

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Given that the diagonal BD the diagonal AC in AO : OC in 3 : 1 To prove : AB = 3CD Proof : in Δ AOC and Δ DOC Δ AOB = Δ COD Δ OBA = Δ ODC (Because DC is parallel to AB, and DB is transversal so these are alternates) Therefore, Δ AOB is similar to COD (By AA similarity) Now, AO/OC = AB/DC (Because in...
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Given that the diagonal BD the diagonal AC in AO : OC in 3 : 1 To prove : AB = 3CD Proof : in Δ AOC and Δ DOC Δ AOB = Δ COD Δ OBA = Δ ODC (Because DC is parallel to AB, and DB is transversal so these are alternates) Therefore, Δ AOB is similar to COD (By AA similarity) Now, AO/OC = AB/DC (Because in similar triangles sides are proportional) 3/1 = AB/DC (Given that AO : OC = 3 : 1) So, AB = 3DC Hence proved. read less
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Given that the diagonal BD the diagonal AC in AO: OC in 3: 1 To prove : AB = 3CD Proof: in Δ AOC and Δ DOC Δ AOB = Δ COD Δ OBA = Δ ODC (Because DC is parallel to AB, and DB is transversal so these are alternates) Therefore, Δ AOB is similar to COD (By AA similarity) Now, AO/OC = AB/DC (Because...
read more
Given that the diagonal BD the diagonal AC in AO: OC in 3: 1 To prove : AB = 3CD Proof: in Δ AOC and Δ DOC Δ AOB = Δ COD Δ OBA = Δ ODC (Because DC is parallel to AB, and DB is transversal so these are alternates) Therefore, Δ AOB is similar to COD (By AA similarity) Now, AO/OC = AB/DC (Because in similar triangles sides are proportional) 3/1 = AB/DC (Given that AO : OC = 3 : 1) So, AB = 3DC Hence proved. read less
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I answered the question in following attachment
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Similar triangles sides are proportional. 3/1=AB/DC (Given that AO:OC=3:1). So, AB =3DC. Hence proved.
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