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To drop a perpendicular to a given line from a given external point. |
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To drop a perpendicular to a given line from a given external point. |
| Given: Line AB and external point P |
| Required: To drop a perpendicular from P to line AB |
| Procedure: |
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With P as a center, use the compass tool to construct a circle
intersecting AB at C and D. |
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With C as a center and with a radius greater than 1/2 CD, use the
compass tool to construct a circle. |
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Label any point on this circle G. |
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Use the segment command under the construct menu
and construct a segment congruent to CG, the circle radius. |
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Use the circle by center + radius command under the construct menu to construct a circle with D as a center and
radius congruent to segment CG. |
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Label the intersection of the two circles that is
on the opposite side of the line as the point P,
point E. |
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Use the segment command under the construct menu and construct segment PE. |
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PE is the required perpendicular. |
| Proof: |
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Since radii of the same circle or equal circles are equal, P and
E are equidistant from C and D. |
PE 
CD |
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PE AB (Two
points each equidistant from the extremities of a line segment determine
the bisector of that line segment.) |
| Sketch: On the sketch below, drag point P around, does the segment stay perpendicular? What condition is not being met when the perpendicular disappears as you drag point P towards B? |
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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. perpendicular from point off a line |
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