Question

Prove that,in an isosceles triangle,the bisector of the vertical angle,the altitude from the vertex and the median to the base are coincident.

Answer 1

Answer:

Proof:  

Consider the two triangles ABD and ACD,  

AB = AC (Given)  

Angle BAD = Angle CAD  (since given AD bisects angle BAC)  

AD = AD (Common sides)  

Thus the two triangles ABD and ACD are consistent (By 'SAS' compatibility adage of triangles)  

therefore angle ADB = edge ADC - (1) (Corresponding parts of  

congruence triangles are equivalent)  

In any case, these two are direct pair that is their entirety is 180 degrees - (2)  

Thus from (1) and (2), every one of the points ADB and ADC are 90 degrees.  

Therefore, AD is perpendicular to BC.