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  • In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see Fig.). Show that ∆ ABC ≅ ∆ ABD. What can you say about BC and BD?

1. In quadrilateral \small ABCD, \small AC=AD and \small AB bisects \small \angle A (see Fig.). Show that  \small \Delta ABC\cong \Delta ABD. What can you say about \small BC and \small BD ?

               

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In the given triangles we are given that:-  

 (i)  \small AC=AD

(ii)  Further, it is given that AB bisects angle A.  Thus \angle BAC  =\ \angle BAD.  

(iii) Side AB is common in both the triangles.  AB=AB

Hence by SAS congruence, we can say that  :   \small \Delta ABC\cong \Delta ABD

By c.p.c.t. (corresponding parts of congruent triangles are equal) we can say thatBC\ =\ BD

 

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Devendra Khairwa

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