In an isoceles triangle ABC with AB=AC, D and Eare points on BC such that BE=CD.Show that AD=AE.
Asked by 2806rahul | 16th Sep, 2009, 04:55: PM
Consider the triangle ΔABC, points D and E can be put on side BC in two ways.
Let's say we put E close to B and D close to C,
then the triangles ABE and triangle ACD are SAS congruent,
since AB = AC........given,
B =
C......angles opposite to equal sides,
and BE = CD ... given,
Hence AD = AE.
Now let's put E close to C and D close to B,
then in triangle ABD and ACE are SAS congruent,
since AB = AC........given,
B =
C......angles opposite to equal sides,
And BD = CE, as shown below,
BE = CD
BE - DE = CD - DE
BD = CE,
Hence AD = AE.
Regards,
Team,
TopperLearning.
Answered by | 30th Sep, 2009, 09:34: PM
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