Explanation Procedure used: STEP 1: We start with the acute triangle A B C . 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 B , one end of that line, draw an arc across the opposite side. Label this point F . Repeat for the other end of the line, C . Label this point P . STEP 3: With the compasses on B , set the compasses width to more than half the distance to P . From B and P , draw two arcs that intersect, creating point Q . STEP 4: Use a straightedge to draw a line from C to Q . The part of this line inside the triangle forms an altitude of the triangle STEP 5: Repeat the process with the compasses on C , set the compasses width to more than half the distance to F . From C and F , draw two arcs that intersect, creating point E . STEP 6: Use a straightedge to draw a line from B to E . The part of this line inside the triangle forms an altitude of the triangle STEP 7: The point where the two altitudes intersect is the orthocenter of the triangle. The point O is the orthocenter of the acute triangle. 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 acute triangle. Construct its orthocenter. Clarification: STEP 1: We start with the acute 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 B , one end of that line, draw an arc across the opposite side

Elementary Geometry For College Students, 7e

7th Edition

ISBN: 9781337614085

Author: Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher: Cengage,

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Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 7.2, Problem 18E

To determine

To draw:

The acute triangle constructs its orthocenter.

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Chapter 7.2, Problem 17E

Chapter 7.2, Problem 19E

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Elementary Geometry For College Students, 7e

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To draw: The acute triangle constructs its orthocenter.

Solution Summary: The author explains how to draw an acute triangle. It constructs its orthocenter.