Identifying Triangle Height: Geometric Line Analysis Problem

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

To solve this problem, we must determine whether the dashed line in the presented triangle fulfills the criteria of being a height. Let's verify each critical aspect:

• First, identify what a height (altitude) is: It is a line drawn from a vertex perpendicular to the opposite side.
• Next, observe the figure. We have a triangle with a dash line drawn from the top vertex to a side that seems to extend from one corner of the base to another point on the extended base.
• Since this line is not shown to be perpendicular to the base of the triangle (no right angle box), we cannot affirm that it fulfills our requirement.

As a result, the straight line does not meet the standard definition of a height for this triangle since it does not form the necessary 90-degree angle with the base. Therefore, as the line is not perpendicular to the opposite side, it is not the height.

Thus, the correct answer to the problem is No.