In an isosceles triangle prove that the altitude from the vertex angle bisects the base - Maths - Lines and Angles

Question

In an isosceles triangle prove that the altitude from the vertex
angle bisects the base

Rahul K · Accepted Answer

Dear Student,

The solution for the question is provided below, the information
provided in picture is not necessary as it can be proved as
below,
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/1910069/2012_05_04_15_43_18/2245062%20png">
Given:
ABC is an isosceles triangle with AB = AC and base BC AD is the
altitude from A
Now in Δ ABD and Δ ACD
∠ADB = ∠ADC =
90° (AD is the altitude)
∠ABD = ∠ACD =
(âˆµAngles opposite to equal sides in
âˆ† ABC)
AB = AC (Given)
So,
âˆ†ABD ≅ âˆ†ACD (by AAS
congruency criterion)
⇒ BD = CD (C P C
T )
⇒ AD bisects
BC
Hence Proved

Regards