Triangle Height Verification: Is the Given Line an Altitude?

Video Solution

Solution Steps

00:00 Determine whether the straight line in the drawing is a height in the triangle

00:03 A height in a triangle extends from one of the triangle's vertices and is also perpendicular to the side

00:08 By drawing possible heights, we can observe that none of them fit the criteria

00:11 Therefore the straight line is not the height, and this is the solution to the question

Step-by-Step Solution

To determine if the given line in the triangle is the height, we need to check if it satisfies the conditions of a triangle's altitude.

Step 1: Identify the base of the triangle. The problem suggests that the horizontal line, presumably at the bottom of the triangle, acts as the base.
Step 2: The altitude must be drawn from the vertex opposite to the base and be perpendicular to this base. Thus, the potential altitude would start at the apex of the triangle.
Step 3: The given figure features a straight line connecting two points on the interior of the triangle and is not perpendicular to the base.

Therefore, this line cannot be the height because it does not extend perpendicularly from the apex opposite the base to the base itself.

Thus, the correct answer is No.