Equilateral Triangle Theorem
Equilateral triangle theorem states that,
“For any equilateral triangle ABC, if P is any point on the arc BC of the circumcircle of the triangle ABC, then PA = PB + PC”
Proof:
In cyclic quadrilateral ABPC, we have,
PA⋅BC = PB⋅AC + PC⋅AB
As ABC is an equilateral triangle,
AB = BC = AC
Thus,
PA.AB = PB.AB + PC.AB
Simplifying,
PA.AB = AB(PB + PC)
PA = PB + PC
Hence, proved.
Equilateral Triangle
Equilateral Triangle is a triangle with all three sides and all three angles equal. As we know a triangle has three angles and three sides, thus in an equilateral triangle all three sides and all three angles are equal. Hence, it is also called a equiangular triangle.
Where each angle measures 60 degrees, similar to other types of triangles. The word equilateral is made of two words “equi” and “lateral” where equi means equal and lateral means side. Thus equilateral triangle means a triangle with equal sides. In this article, we learn about equilateral triangles, their properties of equilateral triangle, their formulas of equilateral triangle, and others in detail.
Table of Content
- What is an Equilateral Triangle?
- Equilateral Triangle Angles
- Equilateral Triangle Formulas
- Shape of Equilateral Triangle
- Properties of Equilateral Triangles
- Equilateral Triangle Theorem
- Equilateral Triangle Formulas
- Height of Equilateral Triangle
- Perimeter of Equilateral Triangle
- Area of Equilateral Triangle
- Area of Equilateral Triangle using Heron’s Formula
- Centroid of Equilateral Triangle
- Circumcenter of Equilateral Triangle
- Equilateral Triangle Symmetry
- Rotational Symmetry
- Reflection Symmetry
- Difference Between Scalene, Isosceles, and Equilateral Triangles
- Examples on Equilateral Triangle
- Practice Questions on Equilateral Triangle
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