How To Find The Bisector Of An Isosceles Triangle | The Science

The Science

# How to find the bisector of an isosceles triangle

In two equal sides of an isosceles triangle, with its base angles are also equal. Therefore bisector carried out to the sides will be equal. Bisector conducted to the base of an isosceles triangle, and is simultaneously median height of the triangle.

## Instruction how to find the bisector of an isosceles triangle

Step 1:

Let AE bisector held BC to the base of an isosceles triangle ABC. AEB is a rectangular triangle as bisector AE will simultaneously be his height. The side AB is the hypotenuse of the triangle, and BE and AE - it katetami.Po Pythagorean theorem (AB ^ 2) = (BE ^ 2) + (AE ^ 2). Then (BE ^ 2) = sqrt ((AB ^ 2) - (AE ^ 2)). Since AE and the median of triangle ABC, then the BE = BC / 2. Consequently, (BE ^ 2) = sqrt. ((AB ^ 2) - ((BC ^ 2) / 4)) If the specified angle at the base ABC, that of a rectangular triangle the bisector AE is AE = AB / sin (ABC). Angle BAE = BAC / 2, as AE - bisector. Hence, AE = AB / cos (BAC / 2).

Step 2:

Now let height BK held to the side AC. This height is no longer either the median or the bisector of the triangle. To calculate the length of the triangle there is a formula Styuarta.Perimetr - is the sum of the lengths of all its sides P = AB + BC + AC. And his semiperimeter equal to half the sum of the lengths of all its sides: P = (AB + BC + AC) / 2 = (a + b + c) / 2, where BC = a, AC = b, AB = c.Formula Stewart for length bisector drawn to the side of c (ie, AB), will take the form of: l = sqrt (4abp (pc)) / (a ​​+ b).

Step 3:

Stewart seen from the formula that the bisector drawn to the side b (AC), will have the same length as b = c.