Question #304c8
2 Answers
Yes.
Explanation:
In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length.
An altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base.
Thus, for an isosceles triangle the median and altitude will be the same for the angle-side pair are from the intersection point of the two sides of equal length.
HenceAD is the median, altitude & angular bisector of the isosceles triangle.
Explanation:
Given : It’s an isosceles triangle with sides
Let AB be the angular bisector of
Using angular bisector theorem,
i.e. AD is the median of BC.
Triangles ACD & ABD are congruent as
#AC = AB, CD = BD, AD common.
Hence AD is also the altitude on CB.
HenceAD is the median, altitude & angular bisector of the isosceles triangle.