Chapter 7.2, Problem 10E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

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?

To determine

(a)

**To find:**

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

Explanation

**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.

To determine

(b)

**To find:**

What point is the orthocenter of any right triangle.

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