Question

prove that two equilateral Triangles will be always similar to each other irrespective of the measurement size by SSS​

Answer 1

As all angles of an equilateral triangle measures 60° ---( By defn.)
Two equilateral triangles are similar to each other by AAA / AA test of similarity of triangles

Answer 2

Answer:

QED

Step-by-step explanation:

Equilateral triangle has all sides equal

in Δ ABC  

AB = AC = BC = X ( Let say)   - Eq 1

now say another triangle

Δ DEF

DE = EF = DF = Y  ( let say)  Eq 2

for two triangles (ΔABC ≅ Δ DEF) to be similar

Corresponding sides ration should be same

AB/DE  = BC/EF = AC/DF

From Eq 1 & Eq 2

AB/DE = X/Y

BC/EF = X/Y

AC/DF = X/Y

Hence

AB/DE  = BC/EF = AC/DF = X/Y

so Both triangle are Similar ≅

QED