If ∆FEC≅∆GDB, ∠1=∠2. Prove that ∆ADE~∆ABC

1.	If ∆FEC≅∆GDB, ∠1=∠2. Prove that ∆ADE~∆ABC
Answer» Given : ∆ FEC ≅ ∆ GBD ,\xa0SO From CPCTWE GET,BD = CE ----------------- ( 1 )ALSO GIVEN : ∠ 1 = ∠ 2 ,SO FROM BASE\xa0ANGLE THEOREM IN ∆ ADEWE GETAD =AE ------------------------ ( 2 )\xa0From equation 1 and 2 we getADBD = AECE , So from converse of B.P.T. we getDE \| \| BCTHEN ,∠ 1 = ∠ 3 ( CORRESPONDING ANGLES AS DE \| \| BC AND AB IS TRANSVERSAL LINE )AND∠ 2 = ∠ 4 ( CORRESPONDING ANGLES AS DE \| \| BC AND AC IS TRANSVERSAL LINE )FROM ABOVE TWO EQUATIONS WE CAN SAY THAT :∆ ADE ~ ∆ ABC ( ByAArule )( Hence proved )

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