What is called the height of an isosceles triangle?

We meet the concept of “height of an isosceles triangle” in the theorem on the bisector, median, height, drawn to the base of an isosceles triangle:

Theorem 2. In an isosceles triangle, the bisector to the base is the median and the height.
Theorem 3. In an isosceles triangle, the median drawn to the base is the bisector and the height.
Theorem 4. In an isosceles triangle, the height drawn to the base is the bisector and the median.
Proof of the theorem:

Given Δ KBC.
From point B we draw the height BM.
The triangle has split into two Δ KBM and ΔCBM. According to the Pythagorean theorem, these triangles are equal, because their hypotenuse and common leg are equal.
Straight lines KC and BM are called perpendicular.
В Δ KBM and Δ BCM ∠ BKM = ∠ BCM (from Theorem 1).
KB = BC – the sides are equal.
Sides KM = CM, because point M divides the segment in half.
Therefore Δ KBM = ΔBCM.
The bisector, height and median are the same segment – BM
It must be remembered that when solving such problems, it is always necessary to lower the height to the base of the isosceles triangle, while division into two right-angled triangles occurs.