which statement is true of all equilateral triangles?
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In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
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Yes. All equiangular triangles are similar. In geometry, we have a nice theorem that allows us to determine if two triangles are similar using the...
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Formulas and Calculations for a equilateral triangle: Altitude of Equilateral Triangle h = (1/2) * √3 * a. Angles of Equilateral Triangle: A = B = C = 60° Sides of Equilateral Triangle: a = b = c.
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A regular polygon must be equilateral (all of its sides are the same length) and equiangular (all of its angles are the same measure). A rhombus is equilateral: all of its sides are of the same length. ... A rhombus can never be a regular polygon because it is not equiangular.
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Are bisectors of an angle always perpendicular? NO, not in all triangles. In an equilateral triangle, XYZ, all the three angles = 60 deg. The bisectors of all the three angles will be perpendiculars on the opposite side and bisect that side.
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Therefore, according to the side-side-side property of triangles, these are congruent. Therefore, the corresponding angles would be equal. ... Thus, the opposite angles in a rhombus are equal.
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All three sides of an equiangular triangle are congruent (same length).
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From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that the triangle APB is equilateral. From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that the triangle APB is equilateral.
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It is a specific kind of isosceles triangle whose base is equal to each leg, and whose vertex angle is equal to its base angles. ... Therefore, since all three sides of an equilateral triangle are equal, all three angles are equal, too. Hence, every equilateral triangle is also equiangular.
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Regular - all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
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There are three types of triangle based on the length of the sides: equilateral, isosceles, and scalene.
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Are All Equilateral Triangles Similar? A regular polygon is one in which all angles are equal and all sides are equal. So by definition, all regular polygons with the same number of sides are similar to each other. An equilateral triangle is a regular polygon with 3 sides, so all equilateral triangles are similar.
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Equilateral triangle indicates that its three sides are equal in length. Equal sides have equal angles at the opposite vertex. So each interior angles is 60°. ... Equilateral triangles are always an acute triangle.
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Answer Expert Verified. ΔPQR is an equilateral triangle because its sides are equal. In a regular hexagon, the r1 or radius of the incircle is equal to the side length of the hexagon.
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The sides of an equiangular triangle are all the same length (congruent), and so an equiangular triangle is really the same thing as an equilateral triangle. See Equilateral Triangles.
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Congruent triangles have corresponding sides of equal length and corresponding angles of equal measure. They are the same exact size and shape. is equilateral and is isosceles, so they are not the same exact shape. ... All congruent triangles are similar, but these triangles are not congruent.
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2 Answers By Expert Tutors All equilateral triangles have the same same shape (three equal sides, three equal angles). ... A hexagon only needs to have six sides. Not all hexagons are the same shape. All hexagons are not similar.