Question

13. In triangle ABC, D and E are points on BC such that BD = CE. IF angle ADE = angleAED, then
prove that A ABC is an isosceles triangle
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Answer 1

Step-by-step explanation:

Since /_ADE is equal to /_AED, side AD is equal to side AE [angles of an isosceles triangle]-(1)

BD=EC

Adding DE on both sides

BD+DE=EC+DE [When equals are added to equals, the sum are equals]

BE=CD-(2)

Consider ∆ABE and ∆ACD,

AD=AE (1)

BD=EC (2)

/_ AEB=/_ADC (given)

=> ∆ABE is congruent to ∆ACD

AB=AC (cpct)

Hope this helped!