君1In figure, ΔFEC ΔGDB and L122. prove that ΔADE ~AABC.OTO

1.	君1In figure, ΔFEC ΔGDB and L122. prove that ΔADE ~AABC.OTO
Answer» Given :∆FEC≅∆GBD , SO From CPCT WE GET, BD=CE----------------- ( 1 ) ALSO GIVEN :∠1 =∠2 , SO FROM BASE ANGLE THEOREM IN∆ADE WE GET AD =AE------------------------ ( 2 ) From equation 1 and 2 we get ADBD=AECE, So from converse of B.P.T. we get DE \| \| BC THEN , ∠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)

Answer»

Given :∆FEC≅∆GBD ,

SO From CPCT

WE GET,

BD=CE----------------- ( 1 )

ALSO GIVEN :∠1 =∠2 ,

SO FROM BASE

ANGLE THEOREM IN∆ADE

WE GET

AD =AE------------------------ ( 2 )

From equation 1 and 2 we get

ADBD=AECE, So from converse of B.P.T. we get

DE | | BC

THEN ,

∠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)

Discussion