Triangle is the minimum sided Polygon. It has three sides and can be categorized as follows: Equilateral triangle, Isosceles triangle, scalene triangle and Right – Triangle. Let us discuss Isosceles Triangle’s Geometry. An isosceles triangle is a triangle with 2 sides or edges equal and therefore two corresponding opposite angles are also equal in measure. If we want to divide the Equilateral Triangle which has three equal sides, in 3 equal parts, it is not possible. The same is possible with the isosceles triangle. Let us see how do you divide an isosceles triangle into 3 equal parts.
For this we need to consider an isosceles triangle ABC as follows:
In the given triangle ABC the sides AB and AC are equal and the third side BC is greater than other two sides AB and AC. To divide the triangle in three equal parts we need to draw two lines from the vertex A to side BC such that they divide the line BC into three equal parts. This will give us three Triangles that are similar to each other. The areas of these triangles will also be same and the sides and angles are proportionate. Thus we draw two lines AD and AE such that we have BD = DE = EC. These lines must bisect the angle BAC in three equal parts i.e. angle (BAD) = angle (DAE) = angle (EAC). Thus we have three triangles ABD, ADE and ADC congruent to each other.
Triangle ABD ≠ Triangle ADE ≠ Triangle ADC,
BD = CE = DE = 1 /3 BC &,
Angle BAD = Angle DAE = Angle EAC = 1 /3 angle BAC,
Remember, this procedure is not possible in case of an equilateral triangle as all the sides of this triangle are equal in measure.