# a) To locate the orthocenter, is it necessary to construct all three altitude of a right triangle? b) What point is the orthocenter of any right triangle?

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
Publisher: Cengage,
ISBN: 9781337614085

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
Publisher: Cengage,
ISBN: 9781337614085

#### Solutions

Chapter
Section
Chapter 7.2, Problem 10E
Textbook Problem

## a) To locate the orthocenter, is it necessary to construct all three altitude of a right triangle?b) What point is the orthocenter of any right triangle?

Expert Solution
To determine

(a)

To find:

To locate the orthocenter, is it necessary to construct all three altitudes of a right triangle.

### Explanation of Solution

Definition:

Orthocenter:

The point where the three altitudes of a triangle meet. An altitude is a line that goes through vertex (corner point) and is at right angles to the opposite side.

Given:

To locate the orthocenter, is it necessary to construct all three altitudes of a right triangle.

Calculation:

By the above definition,

The orthocenter is the point where all three altitudes of the triangle intersect. An altitudes is a line which passes through a vertex of a triangle, and is perpendicular to the opposite side.

The three altitudes all intersect at the same point so we only need two altitude to locate it.

For example:

In a right angle triangle, two sides are perpendicular to each other. The legs of the right triangle are two of the altitudes.

Expert Solution
To determine

(b)

To find:

What point is the orthocenter of any right triangle.

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