Pallabi and Siraj drew the same triangles each of whose two angles is unequal.



Now we will measure the length of the sides from each triangle using a scale, we get

First, consider ΔMAN
We know angles opposite to equal sides are equal, hence in ΔMAN,
Side AM= side MN,
⇒ ∠N=∠A
Hence in this ΔMAN, two angles are equal, so this is not what Pallabi or Siraj drew.

Now we will consider the next triangle, i.e., ΔPAN
In this, no two sides are equal, i.e.,
AN>PN
We know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.
In ΔPAN, ∠P is opposite to side AN, and ∠A is opposite to side PN,
⇒ ∠P>∠A
Hence in these two angles are unequal, so this triangle is drawn either by Pallabi or Siraj.

Now we will consider the next triangle, i.e., ΔFAN
In this, no two sides are equal, i.e.,
FN>AF
We know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.
In ΔFAN, ∠A is opposite to side FN, and ∠N is opposite to side AF,
⇒ ∠A>∠N
Hence in this two angles are unequal, so this triangle is drawn either by Pallabi or Siraj.
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