Geometry

Question Analysis

The main focus is to test the understanding of the definition of the orthocenter by choosing the correct statement among the given options.

Key Concept Explanation

The orthocenter of a triangle is the point where the three altitudes of the triangle intersect. An altitude is a line segment from a vertex perpendicular to the opposite side.

Step - by - Step Solution

1. Analyze each option:

A: “An orthocenter is the line of currency of the altitudes.” This statement has incorrect and non - sensical wording. It is not the correct definition.

B: “An orthocenter is a parallel line.” An orthocenter is not a line at all, let alone a parallel line. So this option is incorrect.

C: “An orthocenter is a perpendicular line.” An orthocenter is not a line; it is a point. So this option is incorrect.

D: “An orthocenter is the point of currency of the altitudes.” The statement is correct as the orthocenter is the point where the altitudes of a triangle are concurrent (intersect).