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 angle BAD = angle CAE, prove that the triangular cutout ABC is
isosceles.
which values are inculcated through this activity?​

Answer 1

Given:

For 'Sarva Shiksha Abhiyan' rally students divided the triangular piece into three parts as shown in the Figure.  

AD = AE and angle BAD = angle CAE

To find:

Prove that the triangular cutout ABC is isosceles.

Solution:

From given, we have,

AD = AE and ∠ BAD = ∠ CAE

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

(we know that, if two sides of a triangle are equal then that triangle is isosceles)

As ∠ ADE is an exterior angle of Δ ADB

so we have,  

∠ ADE = ∠ DBA + ∠ BAD ......... (i)

As ∠ AED is an exterior angle of Δ AEC

so again we have  

∠ AED = ∠ ACE + ∠ CAE  .......... (ii)

using equations (i) and (ii) we have

∠ DBA = ∠ ACE

Therefore, Δ ABC is an isosceles triangle.