Question

In figure 3.59, point D and E are on side BC of △ ABC, such that BD = CE and AD = AE. Show that △ ABD ≅ △ ACE.
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Answer 1

Answer:

In triangle ADE, AD=AE

therefore, triangle ADE=triangle AED (Angles opposite to equal sides)

Now,

angle ADE + angle ADB = 180°...(1)

angle AED + angle AEC = 180°...(2)

Subtracting (2) from (1), we get

angle ADB - angle AEC = 0

= angle ADB = angle AEC...(3)

In triangle ABD and triangle ACE

angle ADE = angle AEC [From(3)]

BD = CE (Given)

AD = AE (Given)

By SAS Test of congruency

Triangle ABD is congruent to triangle ACE.

|| हर हर महादेव ||♡

Answer 2

Required Answer :-

Let us see what is given;

BD = CE and AD = AE.

Now, in ∆ADE,

<ADE= <AED(opposite angles of equal sides of isoceles triangle)

By linear pair,

<ADB = <AEC-------(1)

From (1) and given ;

△ ABD ≅ △ ACE.(SAS criteria)

$:D$

Hope it helped !