Answer: The answer is the altitude.
Step-by-step explanation: We are to state the name of the line segment which is equivalent to the median of an isosceles triangle.
As shown in the attached figure, ABC is an isosceles triangle in which AB = AC. AD is the median to side BC, so D will be the mid-point of BC and hence BD = DC.
In ΔABD and ΔACD, we have
AB = AC,
BD = DC
and
AD is the common side.
Therefore, by side-side-side postulate, we have
ΔABD ≅ ΔACD.
So, ∠ADB = ∠ADC (Corresponding sides of congruent triangles).
Also, by linear pair property,
∠ADB + ∠ADC = 180°.
Therefore,
∠ADB = ∠ADC = 90°, which shows that AD is perpendicular to BC. Thus, AD is an altitude of ΔABC.
So, the complete statement is
The median of an isosceles triangle is the same segment in the triangle as the ALTITUDE.
