Step-by-Step Guide to Geometric Constructions
&
Useful Definitions
1.
Congruent Line Segments:
-draw point and label it c.
-measure the length from endpoint to endpoint on the given line.
-keeping compass open the same distance, place point on point c
and swing an arc to show you measured. Connect point C and new point D to
create a line segment.
2.
Congruent Angles:
-draw reference line and make a starting point on it.
-place compass point on vertex of given angle and open it to
whatever length you want as long as it’s on the angle line. Swing an arc that
crosses AB and BC.
-swing an arc using the same amount of openness on the compass
on your reference line.
-measure the width of the arc on your given angle and swing arc
to show you measured.
-do the same to your reference line and draw a line in the crisscross.
3.
Perpendicular Bisector
-place point
on either endpoint.
-choose any
compass setting that is more than half of the line segment and swing an arc.
-do the same
for the other endpoint, so the arcs intersect.
-draw a line
through the crisscrossing arcs.
4. Bisecting Angles
-Place
point on vertex and swing an arc that crosses both sides of the angle (any
length).
-place
point on one of the intersection points and create an interior arc. Do the same
for the other intersection point so the two arcs crisscross.
-draw
bisector going through crisscrossing interior arcs.
5. Perpendicular Lines to Point on Given
Line
-Label
points A, P, B from left to right on given line segment.
-place
point of compass on point P and swing an arc that intercepts AB. Name intersection
points C and D.
-place
compass point on C and stretch compass more than one half of CD and draw an
arc. Do the same for point D.
-draw
a line through crisscrossing arcs.
6. Perpendicular Lines to Point Outside
Given Line
-same
as #5.
This video is really helpful!!
Orthocenter= intersection of triangles
altitudes.
Circumcenter= where perpendicular bisectors
of a triangle meet; center of a circumscribed circle.
Centroid= intersection of three medians
in a triangle.
Incenter= intersection of angle bisectors
in a triangle.
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