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To divide a given line segment into a given number of equal parts. |
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To divide a given line segment into a given number of equal parts. |
| Given: Line segment AB |
| Required: To divide segment AB into 3 equal parts. |
| Procedure: |
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Use the straightedge tool and draw line AX forming any convenient angle with
AB. |
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Place and label any point C on AX. |
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Use the segment command under the construct menu
and construct segment AC. |
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Use the circle by center + radius command under the construct menu to
construct a circle with center at C and radius congruent to segment AC. |
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Label the intersection of that circle and line AX
point D, and repeat the above with D as center. |
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Label the next intersection point E. (repeat as many times as
needed to generate the number of equal segments wanted.) |
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Use the segment command under the construct menu to construct segment EB. |
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Through points C and D draw lines parallel to EB, label the intersections with AB points F and G respectively.(help)
(Or use the parallel line command under the construct menu.) |
| F
and G divide AB into 3 equal parts. |
| Proof: |
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Since AX is divided into 3 equal parts , AB is divided into 3 equal
parts. (If 3 or more parallels intercept equal
segments on one transversal, they intercept equal segments on every
transversal) |
| Sketch: On the sketch below, dark blue circles were used to lay off the equal segments on AX. Red and green circles constructed the congruent angles. If you change the length of segment AB is it still divided into equal parts? |
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This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use. divide line segment into given number of parts |
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