Question

"For 'Sarva Shiksha Abhiyan' a rally was organised by a school for which students were asked to
prepare slogans on triangular cardboard pieces. They divided the triangular piece into three parts
as shown in the Figure. If AD = AE and ZBAD = ZCAE, prove that the triangular cutout ABC is
isosceles,
nich values are inculcated through this activity?​

Answer 1

Δ ABC is an isosceles triangle. (Proved)

Step-by-step explanation:

See the attached diagram.

Given that AD = AE and ∠ BAD = ∠ CAE

Now, since AD = AE, so Δ ADE is an isosceles triangle and ∠ ADE = ∠ AED.

Now, we have ∠ ADE = ∠ DBA + ∠ BAD ......... (1)

{Since ∠ ADE is an exterior angle of Δ ADB}

Again, we have ∠ AED = ∠ ACE + ∠ CAE  .......... (2)

{Since, ∠ AED is an exterior angle of Δ AEC}

Now, from equations (1) and (2) we get

∠ DBA = ∠ ACE

Hence, Δ ABC is an isosceles triangle. (Proved)