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

Question

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

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
00:06 Therefore this line is not the height, and this is the solution to the question

Step-by-Step Solution

The height of a triangle is defined as the perpendicular distance from a vertex to the line containing the opposite side (base). In this problem, we observe a vertical line segment drawn from a point on the base (horizontal line at the bottom of the triangle) to some level above the base. To determine if this line is a height, it must be perpendicular to the base and also reach to the opposite vertex of the triangle.

In the provided figure, the vertical line extends vertically from the base but does not connect to the opposite vertex of the triangle (at the top). Instead, it terminates at some intermediate point above the base. Since the line does not satisfy the full condition of being perpendicular and reaching an opposite vertex, it cannot be considered the height of this triangle.

Therefore, the given straight line is not the height of the triangle.

The correct and final answer is: No.

Answer

No