In rectangle ABCD, AC is the diagonal.  Show that the diagonal divides it into congruent triangles.

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Dear Student,

Please find below the solution to the asked query:

From given information we form our diagram , As :



In $∆$ ABC and $∆$ CDA 

AB  =  CD                                                ( opposite sides of rectangle are equal to each other )

$\angle$ ABC = $\angle$ CDA = 90$°$                         ( All four angles of rectangle are at 90$°$ )

BC  =  DA                                                ( opposite sides of rectangle are equal to each other )

So,

$∆$ ABC $\cong$ $∆$ CDA                                  ( By SAS rule )                                                            ( Hence proved )
Hope this information will clear your doubts about Congruence of Triangles .

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