Chapter 7.2, Problem 19E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Draw an obtuse triangle and, by construction, find its orthocentre.

(*HINT: You will have to extend the sides opposite the acute angles.)*

To determine

**To draw:**

The obtuse triangle constructs its orthocenter.

Explanation

**Procedure used:**

**STEP 1:** We start with the obtuse triangle

**STEP 2: **Set the compasses width to the length of a side of the triangle. Any side will do, but the shortest works with the compasses on

**STEP 3:** With the compasses on

**STEP 4:** Use a straightedge to draw a line from

**STEP 5: **Repeat the process with the compasses on

**STEP 6: **Use a straightedge to draw a line from

**STEP 7: **The point where the two altitudes intersect is the orthocenter of the triangle. The point

Repeat steps 5, 6 on the third side of the triangle. This will help convince you that all three altitudes do in fact intersect at a single point. But two altitudes are enough to find that point.

**Given:**

Draw an obtuse triangle. Construct its orthocenter.

**Clarification:**

**STEP 1:** We start with the obtuse triangle *ABC*.

**STEP 2: **Set the compasses width to the length of a side of the triangle. Any side will do, but the shortest works with the compasses on

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