Chapter 14.3, Problem 19PSC

To determine

To prove the lines containing the altitudes of given triangle are concurrent.

Explanation of Solution

Given:

The given triangle is ABC as follows-

  

Calculation:

Draw a line parallel to opposite side through each vertex of the triangle as follows-

  

By using the theorem 130 of the textbook-

The point of concurrency of the lines containing the altitudes is called the orthocenter of the triangle.

In the above figure $\overline{AD},\overline{BE}$ and $\overline{CF}$ are concurrent at $O$ .

Therefore, the lines containing the altitudes of given triangle are concurrent.