A triangle is isosceles if two of its sides are of the same length. Per this definition, no isosceles triangle is equilateral, and no equilateral triangle is isosceles. Isosceles Triangle Definition, Formulae, Properties, Solved Examples & Dimensions 1. Further, of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.Indeed, this is the definition given by Euclid himself!:
Joel Reyes Noche notes that many primary school instructors define an isosceles triangle to be one with exactly two congruent sides. However, there are authors who give a different definition of isosceles triangles. Therefore, per this definition, every equilateral triangle must be isosceles. This information should be given to you, or you should be able to measure the lengths. It is found by drawing a perpendicular line from the base to the opposite vertex. The height is the measure of the tallest point on a triangle. From the definitions, further deductions may be made.įor example, in the question above, we have the definition:ĭefinition: An isosceles triangle is a triangle with at least two congruent sides.Īn equilateral triangle has three congruent sides, and three is "at least" two. Find the base and height of the triangle. When one is trying to understand a mathematical idea presented by another, it is important to understand the presenter's definitions. The words we use to describe mathematical ideas are a human invention, hence it is important to recognize that different humans might use the same word to describe different ideas, or different words to describe the same idea.
The primary motivation behind this answer is to make more permanent some of the comments left in response to the question and other answers, as well as to incorporate some ideas from a now deleted answer. NB: I am presenting this answer as a frame challenge.
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