# Geometry Constructions

Topics: Line segment, Angle, Elementary geometry Pages: 5 (1308 words) Published: May 20, 2013
Line Segment
1.) Mark a point R that will be one end of the new line
2.) Place the compass point on one end of the line
3.) Adjust the compass width to the other end of the line 4.) Without changing the compass width, move the compass to point R 5.) Draw an arc near where the end of the new line will be 6.) Pick a point S on the arc to be the endpoint of the new line 7.) Draw a straight line between R and S

Copy an Angle
1.) Mark a point P to be the vertex of the new angle
2.) Draw a ray PQ in any direction and any length. This will be one side of the new angle 3.) Set the compass point on A and adjust it to any convenient width 4.) Draw an arc across both sides of the angle, creating points J and K 5.) Move the compass to P and draw a similar arc, crossing PQ at M 6.) Set the compass on K and set its width to J

7.) Move the compass to M and draw an arc crossing the first, creating point L 8.) Draw a ray PR from P through L

Perpendicular Bisector
1.) Place the compass point on one end of the line
2.) Adjust the compass to just over half the line length
3.) Without adjusting the compass width, draw an arc on each side of the line 4.) Without changing the compass width, repeat for the other end of the line 5.) Draw a straight line between the two arc intersections

Angle Bisector
1.) Place the compass point on the angle's vertex
2.) Set the compass to any convenient width
3.) Draw an arc across each leg
4.) Compass can be adjusted at this point if desired
5.) From where an arc crosses a leg, make an arc in the angle's interior 6.) Without changing the compass width, repeat for the other leg 7.) Draw a straight line from A to where the arcs cross

Parallel Lines
1.) Draw a straight line from A to where the arcs cross
2.) With the compass width about half JR, and the point on J, draw an arc across both lines 3.) Using the same compass width, repeat at point R
4.) Set the compass width to the lower arc
5.) Move the compass to the upper arc. Mark off an arc to make point S 6.) Draw a straight line through R and S

Triangle Incenter
1.) With the compass on a vertex, adjust its width to a medium setting 2.) Draw an arc across each leg
3.) Draw two intersecting arcs, one from each previous arc 4.) Draw the angle bisector line
5.) Repeat for one of the other vertices

Triangle Circumcenter
1.) Draw the perpendicular bisector of the side AB
2.) Draw the perpendicular bisector of the side BC
3.) Mark the points where the bisectors intersect as 'O'

Triangle Orthocenter
1.) Set the compass width to the length of a side of the triangle 2.) From B draw an arc across AC creating point F
3.) From C draw an arc across BA creating point P
4.) Set the compass width to more than half the distance BP 5.) From B and P, draw arcs that intersect at point Q
6.) With a straightedge on C and Q, draw an altitude of the triangle 7.) Set the compass width to more than half the distance CF 8.) From C and F, draw arcs that intersect at point E
9.) With a straightedge on B and E, draw another altitude of the triangle Triangle Centroid
1.) Construct the perpendicular bisector of PQ to find its midpoint S 2.) Draw the first median from the midpoint S to the opposite vertex 3.) Find the midpoint T of another side of the triangle

4.) Draw a second median from the midpoint T to the opposite vertex Copy an angle using SSS
1.) Mark a point A that will be one vertex of the triangle 2.) Set the compass width to the desired length AB
3.) Move to A and draw an arc near the future point B
4.) Mark a point B somewhere on this arc
5.) Set the compass width to desired length of side AC
6.) From A draw an arc near the future third vertex of the triangle 7.) Set the compass width to desired length of side BC
8.) From B, draw an arc...

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