Question

If ∆ABC and ∆XYZ are equilateral triangle and AB=XY, the conditions under which ∆ABC=~∆XYZ

Answer 1

Equilateral Triangle is nothing but, The triangle in which all the sides are equal,

In Triangle ABC, We can say that, 
(1) AB = BC = CA, Since it is equilateral triangle, and since all the sides are equal,

Now, 
In Triangle XYZ, We can say that,
(2) XY = YZ = ZX, Since it is equilateral triangle, and since all sides are equal,

Now, According to the question,
AB = XY, From this, we can say that,
BC = YZ, and,
CA = ZA, From (1) and (2)

Now, We also know that there is an axiom known as SSS Axiom,

SSS axiom states that, There exists only 1 triangle with 3 sides given,
Which means, From this axiom, we can say that Triangle ABC and Triangle XYZ are equal that is congruent,

=> ΔABC ≅ ΔXYZ,

Therefore by SSS Axiom we can say that both the triangles are similar, This is the condition by which we can say !

Hope you understand, Have a Great day and Advance Merry Christmas !
Thanking you, Bunti 360 !

Answer 2

Answer:

here your answer. I hope its help you