Question

Triangle ABC is isosceles with
AC=BC and Points D and E are chosen on segment AB so that
AD=DE=EB
find angle CDE in degrees

Answer 1

Answer:

Given ABC is an isosceles triangle with AB=AC .D and E are the point on BC such that BE=CD

Given AB=AC

∴∠ABD=∠ACE (opposite angle of sides of a triangle ) ....(1)

Given BE=CD

Then BE−DE=CD−DE

ORBC=CE......................................(2)

In ΔABD and ΔACE

∠ABD=∠ACE ( From 1)

BC=CE (from 2)

AB=AC ( GIven)

∴ΔABD≅ΔACE

So AD=AE [henceproved]