Question

prove that all side of triangle are equal​

Answer 1

Step-by-step explanation:

i think you mean equilateral triangle

let triangle ABC be 30-60-90 triangle

after construction the figure will look like in the above picture pinned with answer

to prove : in triangle ACD all sides are equal

solution:-

in triangle ABC and DBC

side BC is congruent to side BC(common)

angle CBA is congruent to angle CBD,(EACH ANGLE 90°)

side AB is congruent to side DB(construction)

therefore triangle ABC is congruent to DCB by SAS test of congruency

now,

ACB is congruent to BCD(cact)

BAC is congruent to BDC(cact)

in triangle ACD

all angles are 60°

so it is equilangular

but equilangular triangles are equilateral triangle also

therefore triangle ACD is equilateral triangle means it's all sides are equal

hence proved