you measure all the sides
Not necessarily. You have described "similar" triangles. If you also know that any of the lengths of sides are of equal measure in addition to three angles (congruent), then the lengths of all of the sides are of equal measure. But with what you have given, consider, for example, two equilateral triangles, both have all angles equal to 60 degrees (satisfying the condition in your question). One of the triangles could have sides length 1 and the other with sides all of length 2.
Three triangles
The congruence theorems for right triangles are the Hypotenuse-Leg (HL) theorem and the Leg-Acute Angle (LA) theorem. The HL theorem states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. The LA theorem states that if one leg and one acute angle of one right triangle are congruent to one leg and one acute angle of another right triangle, then the triangles are congruent.
If all of the diagonals are drawn from a vertex of an octagon, how many triangles are formed
All isosceles triangles are not equilateral triangles
5 triangles are formed.
You Can Get 6 triangles
3 triangles
As many as you like but they will all be scalene triangles
Yes all equilateral triangles are acute triangles, but not all acute triangle are equilateral triangles.
All isosceles triangles are not equilateral triangles