It is called the circumcircle of the triangle.
You might have first noticed the circle on which the vertices of the triangle A, B, and C all lie. Only moving A, B, or C will actually change the shape of the triangle. An exception is G itself, and if you move it, the figure will slide along with it. If you drag any other point, the figure is designed to Incidentally, you can drag around other points besides the vertices A, B, and C. It can be shown that the centroid trisects the medians, that is to say, the distance from a vertex to the centroid G is twice the distance from the centroid to the opposite side of the triangle. If you make a real triangle out of cardboard, you can balance the triangle at this point. Other names for the centroid are the barycenter and the center of gravity of the triangle. This point is called the centroid of the triangle. Notice that they all meet at one point G in the triangle, also colored green. The medians of this triangle are AA', BB', CC', and they’re colored green. A line connecting a vertex of the triangle to the midpoint of the opposite side is called a median of the triangle. You can move and resize the window that appears.) The midpoint of the side BC is A', the midpoint of the side CA is B', and the midpoint of the side AB is C'. (By the way, you can place your mouse cursor over the diagram and press the return key to lift the diagram off the page. It is the only triangle that has angles in the proportion 1:1:2 and has angles of 36°, 72°, and 72°.Along the sides of the triangle, you see the midpoints labelled A', B', and C'. The golden triangle is an acute isosceles triangle where the ratio of twice the the side to the base side is the golden ratio.The Morley triangle is a special equilateral (and thus acute) triangle that is formed from any triangle where the vertices are the intersections of the adjacent angle trisectors.If C is the greatest angle and h c is the altitude from vertex C, then the following relation for altitude is true for an acute triangle:įor an acute tirangle with angles A, B, and C: In an acute triangle, the following is true for the length of the sides:Ī 2 + b 2 > c 2, b 2 + c 2 > a 2, c 2 + a 2 > b 2 The longest side of an acute triangle is opposite the largest angle.Acute triangles can be isosceles, equilateral, or scalene.Any triangle in which the Euler line is parallel to one side is an acute triangle.The other two vertices of a square are on the two remaining sides of the acute triangle. Each square coincides with a part of a triangle side. An acute triangle has three inscribed squares.An equilateral triangle has three sides of equal length and three equal angles of 60°. All equilateral triangles are acute triangles.In other words, all of the angles in an acute triangle are acute. Sam Edwards/Getty Images Acute Triangle DefinitionĪn acute triangle is defined as a triangle in which all of the angles are less than 90°. The smallest perimeter triangle with integer length sides is obtuse, with sides 2, 3, and 4.The Calabi triangle is the only non-equilateral triangle where the largest square fitting in the interior can be positioned in three different ways.To find the height of an obtuse triangle, you need to draw a line outside of the triangle down to its base (as opposed to an acute triangle, where the line is inside the triangle or a right angle where the line is a side).įor an obtuse triangle with angles A, B, and C:
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