Question

in an isosceles triangle ABC ,AB=AC,D and E are the points on BC such that BE=CD show that AD =AE
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Answer 1

Answer:

Step-by-step explanation:

In ΔABE and ΔACD,

          AB=AC {given}

          BE=CD {given}

         ∠ABE=∠ACD {angles opposite to same sides AB and AC are equal}

by SAS congruence criteria, ΔABE ≅ ΔACD.

          AE=AD by cpct [corresponding parts of congruent triangles]

                                                                                             hence proved.....

hope it helps you...

       

Answer 2

Solution :-

In ∆ ABD and ∆ ACE ,

⠀AB = AC ⠀⠀⠀⠀⠀⠀(1)

⠀∠B = ∠C ⠀⠀⠀⠀⠀⠀(2)

Also ⠀⠀⠀BE = CD

so , ⠀⠀⠀BE - DE =CD- DE

That is⠀⠀⠀ BD = CE. (3)

so, ⠀⠀⠀⠀∆ABD ≅ ∆ ACE

[using (1),(2),(3) and SAS rule]

⠀⠀⠀⠀⠀This gives AD = AE