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

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

The triangle's altitude is a line drawn from a vertex perpendicular to the opposite side. The vertical line in the diagram extends from the triangle's top vertex straight down to its base. By definition of altitude, this line is the height if it forms a right angle with the base.

To solve this problem, we'll verify that the line in question satisfies the altitude condition:

• Step 1: Identify the triangle's vertices and base. From the diagram, the base appears horizontal, and the vertex lies directly above it.
• Step 2: Check the nature of the line. The line is vertical when the base is horizontal, indicating perpendicularity.
• Conclusion: The vertical line forms right angles with the base, thus acting as the altitude or height.

Therefore, the straight line depicted is indeed the height of the triangle. The answer is Yes.