![]() He distinguishes the three types of triangles:equilateral (3 congruent sides), isosceles (2 congruent sides but not thethird), and scalene (no two congruent). Similarly, a square is a special rectangle - but it is a rectangleand a parallelogram.Įuclid Book I, Definition 20 makes it clear that isosceles triangles haveexactly two congruent sides (the "legs") and one side of a different length(called the "base"). ![]() a theorem about the diagonals bisecting one another). But it is a parallelogram, and any theorem aboutparallelograms applies immeditately to a rectangle. That means you can apply the Isosceles Triangle Theorem and conclude that the three anglesof an equilateral triangle are also equal!Ī similar thing happens with words like 'square' 'rectangle'and parallelogram.Ī rectangle is a special type of parallelogram - with all anglesequal to 90. Yes an equilateraltriangle is an isosceles triangle - for each of the three possible pairs of sides. The standard way these things are handled in math is to treatdefinitions in an inclusive sense. The definition you gave is better because it is explicit.ĭoes your text give a definition of a rectangle? Is a square also a rectangle? An equilateral triangle has two congruent sides, in fact it has three. Thus a triangle with all sides congruent is both isosceles and equilateral.Įven if the definition were worded "An isosceles triangle is a triangle with two congruent sides" I would say that an equilateral triangle is also an isosceles triangle. With your definition it is explicit that any triangle with at least two congruent sides is isosceles. The dictionaries that I looked in defined isosceles as "having two equal sides", leaving it to the reader to interpret whether or not this means exactly two. I first want to compliment whoever made the definition that you gave me, "An isosceles triangle is a triangle with at LEAST two congruent sides". ![]() The question is, if an isosceles triangle only requires at Least two of the sides to be congruent, could an equilateral triangle be called an isosceles triangle? The definiton of an isosceles triangle is a triangle with at LEAST two congruent sides. The definition of an equilateral triangle is a triangle with three congruent sides. The table below compares these three triangles with respect to sides, angles and altitudes.In defining the types of triangles, our class was stumped by a question asked by one of the student. ![]() By familiarising ourselves with these contrasts, we can properly distinguish each type we are dealing with and perform the correct calculations. In this final section, we shall look at the differences between these three triangles. There are three types of triangles we shall often see throughout this syllabus, namely Noting that the sum of the interior angles of a triangle is 180 o, we obtain ∠X = ∠B = ∠D = ∠Z since the vertex angle for triangles ACB and DCE are equal. We know that if two sides of a triangle are congruent the angles opposite them are also congruent. Given the triangles ACB and DCE below, determine the value of angles X, Y and Z if AC = BC, DC = EC and ∠ACB = 31 o.Īs ∠Y and ∠ACB are vertical angles then ∠Y = ∠ACB = 31 o. ![]()
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