In page 148 Qn. 3
BD and CE are altitudes of Triangle ABC such that BD=CE.
1. State the 3 pairs of equal parts in triangles CBD and BCE ?
2. Is triangle CBD congruent to triangle BCE?
3. Is Angle DCB=Angle EBC ?

Dear Student,

Please find below the solution to the asked query:

From given information we form our diagram , As :



Here ,  BD and CE are altitude , So $\angle$ CED  =  $\angle$ BDC  = 90$°$                        --- ( 1 )

1 ) 3 pairs of equal parts in triangles CBD and BCE :

BD  =  CE                                                                       ( Given )

$\angle$ BDC  =  $\angle$ CED  = 90$°$                                               ( From equation 1 )

And

BC  =  BC                                                                       ( Common side )

2 ) $∆$ CBD  $\cong$ $∆$ BCE                                                     ( By RHL rule )


3 ) $\angle$ DCB = $\angle$ EBC                                                        ( By CPCT )


Hope this information will clear your doubts about Congruence of Triangles.

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