Triangle Height Verification: Analyzing a Geometric Construction

Question

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

Video Solution

Solution Steps

00:04 Let's find out if the line in the drawing is a height in the triangle.

00:08 A height starts from one vertex, and goes straight down to meet the opposite side at a right angle.

00:14 This line doesn't start from a vertex, and it's not perpendicular to the side.

00:19 So, this line isn't a height. And that's how we solve this question!

Step-by-Step Solution

To determine if the given straight line is the height of the triangle, we need to check whether it is perpendicular to the side it intersects (or its extension), which is the definition of a height (altitude) in a triangle.

Looking at the figure, the straight line is drawn from a vertex of the triangle to a point on the opposite side, but it is not perpendicular to that side or its extension. Therefore, the line does not meet the criteria for being a height of the triangle.

In conclusion, the line is not the height of the triangle because it is not perpendicular to the opposite side.

Therefore, the correct answer to the problem is No.

Answer

Related Subjects

The Sum of the Interior Angles of a Triangle The sides or edges of a triangle Triangle Height Exterior angles of a triangle Median in a triangle Center of a Triangle - The Centroid - The Intersection Point of Medians All terms in triangle calculation