MathsIsosceles Triangle and Equilateral Triangle – Proof of Theorem

Isosceles Triangle and Equilateral Triangle – Proof of Theorem

About Triangles

A triangle is a three-sided polygon. The sum of the angles in a triangle is 180 degrees. The three angles in a triangle can be named using any three of the following letters: A, B, and C. The angle in the corner of a triangle is always A. The angle next to the angle in the corner is always B. The angle opposite the angle in the corner is always C.

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    Isosceles Triangles

    An isosceles triangle is a triangle with two sides of equal length. These triangles are named for their isosceles shape, which is created when both of the triangle’s base angles are equal in size. This shape is also often referred to as an equilateral triangle, although not all isosceles triangles are equilateral.

    Properties of Isosceles Triangle:

    A triangle is said to be isosceles if it has two sides of the same length. These two sides are called the base and the height. The third side is called the vertex.

    The base and height of an isosceles triangle are always the same length. The vertex is always the longest side of the triangle.

    An isosceles triangle has two angles that are the same size. These angles are called the base angles. The third angle is called the vertex angle.

    The base angles of an isosceles triangle always add up to 180 degrees.

    Isosceles Triangle Theorem:

    In an isosceles triangle, the two base angles are equal.

    Proving of Theorem

    Theorem is proved by contradiction. Suppose that there exists a real number $x$ such that $x

    eq a$ for all $a$. We will show that this leads to a contradiction.

    Since $x

    eq a$ for all $a$, there must be a number $y$ such that $x-y=a$. But then $x=y+a$, which is a contradiction. Therefore, there cannot be a real number $x$ such that $x

    eq a$ for all $a$.

    Facts About Isosceles Triangle

    A triangle is isosceles if it has two sides of equal length. These two sides are called the base and the height. The third side is called the vertex.

    Uses of Triangle

    Triangles are used in a variety of ways. Some common uses of triangles are in roofing, in metalworking, and in construction. Triangles are also used in navigation and in mathematics.

    Equilateral Triangles

    Each of the three angles of an equilateral triangle are 60°.

    Properties of Equilateral Triangle

    An equilateral triangle is a triangle that has all three sides of the same length. The angles of an equilateral triangle are also all 60 degrees.

    Isosceles Triangle Theorem:

    In an isosceles triangle, the two sides that are the same length are called the base and the height. The base is the side that is across from the angle that is not the right angle. The height is the length of the line segment from the base to the vertex of the triangle.

    Solved Example-

    2

    A bag contains 5 red balls and 5 green balls. If two balls are drawn at random, what is the probability that they will both be red?

    The probability that the two balls drawn at random will both be red is 5/10.

    Difference between Isosceles Triangle, Equilateral Triangle, and Scalene Triangle

    An isosceles triangle has two equal sides. An equilateral triangle has three equal sides. A scalene triangle has three unequal sides.

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