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# equilateral triangle rotational symmetry

From Wikipedia

Equilateral triangle - Wikipedia, the free encyclopedia

An equilateral triangle is the most symmetrical triangle, having 3 lines of reflection and rotational symmetry of order 3 about its center. ...

Question:Does anyone know any type of triangles that have a rotational symmetry of 2, and 3? Thanks!

Answers:equilateral triangle has rotational symmetry of 3. (Rotate it 1/3 of a turn and it maps exactly onto itself). No triangle has rotational symmetry of 2. Any non-equilateral triangle has at least one unique angle (and side), so it has no rotational symmetry.

Question:I am a little confused as to what rotational symmetry is???? for example, I cannot figure out with things like 1) a tiger's face 2) a maple leaf 3) a circle have rotational symmetry? please and thanks

Answers:an object has rotational symmetry if after rotating it a given amount(not 360 degrees), it is identical to the starting position. Take a square, rotate it 90 degrees, and it is still a square with the same side positions. An equilateral triangle and 120 degrees is the same. A tiger's face cannot be rotated any less than 1 full rotation and still look the same as the original face(upside down does not count), and neither can a maple leaf. However, a circle can be rotated by any angle and still be symmetrical, so it has infinite rotational symmetry.

Question:In an equilateral triangle, do the 3 lines of symmetry bisect each other? or is there any other relationship between the lines of symmetry ? Yes, i know they bisect the sides of the triangle (duh) but DOES ONE LINE OF SYMMETRY BISECT THE OTHER LINE OF SYMMETRY??

Answers:The three lines of symmetry in an equilateral triangles are the perpendicular bisectors ( they are the medians and the altitudes) and also the angle bisectors. The intersection point divides any altitude into a 2 to 1 ratio.

Question:how many lines of symmetry does an equilateral triangle have 3 2 6 4

Answers:3. the line of symmetry would be the angle bisector of each of the 3 angles.