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Question

In the alongside diagram, ABCD is a parallelogram, then AB=2BC
183005_a1ed14905673480db1af36c490ef24b8.png

A
True
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B
False
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Solution

The correct option is A True
GivenABCDisaparallelogram,ADBC&ABDC,CBE=EBA=1,DAE=EAB=2ConstructionDrawEFfromEsuchthatEF=BC&EFBC.SoBCEFisaparallelogram.SinceEF=BC&EFBCsoEF=AD&EFAD.NowCBE=BEF=1{AlternateangleswhenEFBC,BEisthetransversal}SoBEF=EBF=1EFBisaisoscelestriangle{Sincebaseanglesareequal}inEFB,EF=FBFB=BC(1)NowFEA=EAD=2{AlternateangleswhenEFAD,EAisthetransversal}SoFEA=EAF=2EABisaisoscelestriangle{Sincebaseanglesareequal}inEAB,EF=AFAF=BC(2)Adding(1)&(2),wegetFB+AF=BC+BCAB=2BC
315789_183005_ans_6cccf2123e5640058b2bb8c7a5d8726a.png

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