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DFN: we call a triangle equilateral if all sides of the triangle are the same length
DFN:we call two triangles similar if corresponding angles are equal, and corresponding sides are proportional.
First show that all corresponding sides are proportional:
Consider a equilateral triangle with side lengths 1, all other equal lateral triangles sides can be expressed as S*(1), where S is some scalar. Hence all equilateral triangles sides are proportional to each other.
Next, show that all corresponding angles are equal:
The angle between two sides of a triangle is related to the length of the sides. These relationships are called sin, cos, and tan. Knowing that the cos(x), where x is one of the angles in the triangle, is the adjacent divided by the hypotenuse we see that cos(x)=(1/2)c/a, since a = c (because its equal lateral) we are left with cos(x)=(1/2) which means x = 60 degrees. this can be applied to all three angles, which shows that all three angles are 60 degrees.
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c
We have now shown that all equal lateral triangles are similar because they all have proportional sides, and they all have equal angles.
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Some equilateral triangles are not isosceles?
All isosceles triangles are not equilateral triangles
Are all equilateral triangles acute triangles?
Yes all equilateral triangles are acute triangles, but not all acute triangle are equilateral triangles.
Are all equilateral triangles are congruent?
no. if one triangles sides are all 2 and one triangles sides are all 3 then they are not congruent
All isosceles triangles are also equilateral triangles?
No, all isosceles triangles are not equilateral triangles. An isosceles triangle is a triangle that has two sides of equal length. An equilateral triangle is a triangle that has all three sides of equal length. Therefore, it is possible for a triangle to be isosceles but not equilateral. For example, a triangle with sides of lengths 3, 3, and 4 is an isosceles triangle, but it is not an equilateral triangle because all its sides do not have the same length. On the other hand, all equilateral triangles are also isosceles triangles because they have two sides of equal length. My recommendation ʜᴛᴛᴘꜱ://ᴡᴡᴡ.ᴅɪɢɪꜱᴛᴏʀᴇ24.ᴄᴏᴍ/ʀᴇᴅɪʀ/372576/ꜱᴀɪᴋɪʀᴀɴ21ᴍ/
Are all isosceles triangles also equilateral triangles?
No, not at all, all isosceles triangles aren't equilateral since an equilateral triangle is a triangle with all of its sides equal, i.e. all sides of an equilateral triangle are equal, but in an isosceles triangle only two of its sides are equal.
