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| 1. |
If one diagonal if trapezium cuts the other diaganol in the ratio 1:3 |
| Answer» DE = EB = 1:3In {tex}\\triangle{/tex}AEB and {tex}\\triangle{/tex}CED,\xa0{tex}\\angle 1 = \\angle 2{/tex} (alternate angles)\xa0{tex}\\angle 3 = \\angle 4{/tex}\xa0(Vertically opposite angles.){tex}\\therefore \\quad \\Delta \\mathrm { AEB } \\sim \\Delta \\mathrm { CED }{/tex}{tex}\\Rightarrow \\quad \\frac { \\mathrm { AB } } { \\mathrm { CD } } = \\frac { \\mathrm { BE } } { \\mathrm { DE } } \\Rightarrow \\frac { \\mathrm { AB } } { \\mathrm { CD } } = \\frac { 3 } { 1 }{/tex}\xa0[{tex}\\because {/tex}\xa0DE: BE = 1:3]{tex}\\Rightarrow{/tex}\xa0AB = 3CD | |