True or False, dividing an equilateral triangle into two even parts always results in two 30-60-90 triangles?

True or False? Also, while I have your attention, if one of the sides is equal to something*sqrt(3) does it mean its a 30-60-90 triangle?True or False, dividing an equilateral triangle into two even parts always results in two 30-60-90 triangles?
Hey there!





True. If you draw an altitude that divides an equilateral triangle into two congruent triangles, each triangle is a 30掳-60掳-90掳 triangle.





By the 30掳-60掳-90掳 Triangle Theorem:





short leg * 2 = hypotenuse


short leg * sqrt(3) = long leg





Conversely, if the triangle satisfies any one of the above statement, then it is a 30掳-60掳-90掳 triangle.





Hope it helps!True or False, dividing an equilateral triangle into two even parts always results in two 30-60-90 triangles?
False. You can just lop the top of the triangle and end up with a smaller equilateral triangle equal in area to the trapezium remaining.
Not necessarily. If you chop one half of the area parallel to one side you wind up with an equilateral triangle and a trapezoid. You could also chop it at some other angle and wind up with an irregular triangle and an irregular quadrilateral.





However, if you chop it into two congruent pieces you will have two 30-60-90 triangles.





The second part is not necessarily true either, since any number is sqrt(3) times some other number; so that's really not a restriction at all.
true
True. And the second part is true in most cases.
yup
True if you divide the triangle into triangles.





The second part is true only if ';something'; is equal to the short leg of the triangle.
No to the second part! You would have to know the length of two sides to determine angles.