Question

the line joining the point of intersection of two angular bisectors of the base angles of an isosceles triangles to the vertex bisects the vertical angle

Answer 1

Given : line joining the point of intersection of two angular bisectors of the base angles of an isosceles triangles to the vertex

To Find :  This line bisects the vertical angle

Solution:

Let say ABC with Base BC

AB = AC

=> ∠B = ∠C

BX  & CX  are angle bisector of ∠B  and ∠C

=> ∠ABX = ∠CBX  = ∠ACX = ∠BCX   = ∠B/2 = ∠C/2

in Δ XBC

∠CBX = ∠BCX

=> CX = BX

Compare ΔABX  and ΔACX

AB = AC    ( equal side of isosceles triangle)

∠ABX  = ∠ACX      ( Shown above )

BX  = CX   ( Shown above )

=> ΔABX  ≅ ΔACX

=> ∠BAX = ∠CAX

hence AX bisect  the vertical angle

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Answer 2

Answer:

prove that the line joining the point of intersection of two angular bisectors of the base angles of an isosceles triangle to the vertex bisects the vertical angle