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No. All equilateral and equiangular triangles are acute. (All angles are equal to 60°, which is less than a right angle [90°]); however, the converse (which is what was asked) is not true.
A triangle can have all three angles be less than 90°, but not be an equilateral triangle.
An example is a triangle with angles of 80°, 60°, and 40°. It is scalene and acute.
From the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C), you can show that sin(80°) does not equal sin(60°) or sin(40°), so none of sides a, b, and c, are equal.
You could have an acute isosceles triangle like: 80°, 80° and 20° angles, as another example. From the Law of Sines, you can show that two of the sides are equal, but the third side (opposite the 20° angle) is not equal to either of the other 2.
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what- an equilateral triangle is used in a tent design. is this statement true or false the triangle is equilateral?
true
An equilateral triangle is a special case of an isosceles triangle?
true
Ture or false is An equilateral triangle a special case of an isosceles triangle?
true
True or false a triangle can be both right-angled and equilateral?
False. All angles of an equilateral triangle are 60 degrees.
Is a triangle a small regular polygon?
A regular polygon is any polygon that has sides which are the same length and angles whose measures are equal. An equilateral triangle (also equiangular triangle) is a regular polygon. Other isosceles triangles (equilateral triangles are isosceles, but they are an exception) and scalene triangles are not regular polygons. A side note: Only in a triangle is a polygon regular solely if it is equilateral. (Since an equilateral triangle is equiangular as well). This is NOT always true in other polygons, like quadrilaterals, where it can be equilateral but not necessarily equiangular (a rhombus) or equiangular but not equilateral (a rectangle).
