State the following statement is true or false.

In an isosceles triangle, any two angles of a triangle are the same.

Question

State the following statement is true or false.In an isosceles triangle, any two angles of a triangle are the same.

Accepted Answer

The closed curve which is formed only by joining a finite number of line segments is called a polygon and the point of intersection of line segments is called the vertex. Any line segment which joins to form the polygon is called edge or side. The angles subtended by any two sides is called the angle of the polygon. A triangle is a polygon with three sides and three vertices otherwise known as 3-gon. If we denote the vertices of any triangle as A, B, C then its sides are denoted as

AB
    ¯
   
   ,
    
     BC
    ¯
   
   ,
    
     AC
    ¯

and the length of the sides are denoted as AB,BC,AC. If the lengths of the triangle are not equal to each other which means AB ≠ BC ≠ AC then it is called a scalene triangle.The angles of the triangle ABC are ∠ABC, ∠ACB, ∠BAC. The angles opposite to sides of length AB, AC, BC have the measure denoted as

m∠ACB,m∠ABC,m∠BCA
   respectively.If the lengths of any two sides are equal we call the triangle isosceles triangle which means one of AB = BC, BC = AC, AB = AC in triangle ABC is true. We draw the figure of an isosceles triangle with AB = AC.We know that the angels opposite to sides of equal length have equal measures which means if AB = AC then

m∠ACB=m∠ABC
  . In the above triangle, we have

m∠ACB=m∠ABC
   but we do not have

m∠ACB=m∠BAC
   or

m∠ABC=m∠BAC
  . So if we choose any two angles they may not be equal which means the statement ‘In an isosceles triangle any two angles of a triangle are the same’ is false.

State the following statement is true or false.

In an isosceles triangle, any two angles of a triangle are the same.

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