Triangle Altitude Verification: Is the Given Line a True Height?

Is the straight line in the figure the height of the triangle?

To determine if the straight line in the figure is the height of the triangle, we must verify the following:

• The line segment must extend from a vertex of the triangle and be perpendicular to the opposite side (or its extension).

In examining the figure provided, we notice that the triangle is formed by vertices at points $A, B,$ and $C$. Let's assume the base is the line segment $\overline{BC}$.

The line in question extends from a vertex $A$ and appears to intersect the base $BC$ at a right angle.

• Since it is extending from vertex to the opposite side and forming a right angle with it, this line meets the definition of an altitude.

Therefore, the line in the figure is indeed the height of the triangle. By confirming the perpendicular relationship, we determine that this geometric feature correctly describes an altitude.

Yes, the straight line in the figure is the height of the triangle.