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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

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 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. 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 obtuse 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 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 B, one end of that line, draw an arc across the opposite side

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