Geometric Constructions
In this activity, you will be doing constructions you can do with compass and a straightedge but you will use technology (Geogebra) to perform your constructions.
Congruent Segment
1) Using the compass tool, create a circle with radius length AB.
2) Drag the circle onto ray CD, with point C as the center.
3) Using the intersect tool, mark the intersection of your circle and ray CD, as point E
4) Using the segment tool, mark the segment CE
Segment AB is congruent to segment CE
Congruent Segment
Use the same steps as above create a congruent segment to segment AB.
Congruent Segment
Use the same steps as above create a congruent segment to segment AB.
Congruent Segment
Midpoint/Perpendicular Bisector
1) Using the Compass tool, draw a circle with center A and radius AB
2) Using the Compass tool, draw a circle with center B and radius AB
2) Using the Line tool, draw line CD through the two intersections of the circles
3) Using the Intersection tool, mark the intersection of line CD as E
Line CD intersects line AB at its midpoint, therefore, line CD is the bisector of segment AB, It is also perpendicular!
Midpoint/Bisector
Follow the same steps as above to construct the midpoint and perpendicular bisector of the given segment.
Midpoint/Perpendicular Bisector
Follow the same steps as above to construct the midpoint and perpendicular bisector of the given segment.
Midpoint/Perpendicular Bisector
Line Perpendicular to a Given Line Through a Point Not on the Line
1) Using the tool Circle with center through a point, construct a circle with Center C, such that the radius is longer than the distance from point C to line AB
2) Using the Intersection tool, mark the two intersections of your circle and the line as E and F.
3) Follow the same steps from the Midpoint/Perpendicular Bisector Tasks to construct the perpendicular bisector of line segment EF.
You have constructed a line perpendicular to line AB, through point C
Line Perpendicular to a Given Line Through a Point Not on the Line
Follow the same steps as above to construct a line perpendicular to a given line through a point not on the line.
Line Perpendicular to a Given Line Through a Point Not on the Line
Follow the same steps as above to construct a line perpendicular to a given line through a point not on the line.
Line Perpendicular to a Given Line Through a Point Not on the Line
Line Perpendicular to a Given Line Through a Point on the Line
1) Using the tool Circle with center through a point, construct a circle with Center C
2) Using the Intersection tool, mark the two intersections of your circle and the line as E and F.
3) Follow the same steps from the Midpoint/Perpendicular Bisector Tasks to construct the perpendicular bisector of line segment EF.
You have constructed a line perpendicular to line AB, through point C
Line Perpendicular to a Given Line Through a Point on the Line
Follow the same steps as above to construct a line perpendicular to a given line through a point not on the line.
Line Perpendicular to a Given Line Through a Point on the Line
Follow the same steps as above to construct a line perpendicular to a given line through a point not on the line.
Line Perpendicular to a Given Line Through a Point on the Line
Congruent Angle
1) Using the Compass tool, construct circle B with radius BC.
1a) Click so this circle stays in place.
1b) Using the Intersection tool, mark the intersection of circle B and ray BA as point F
1b) Create a copy of circle B by clicking on the edge of it
3) Bring circle B to point D, making D the center of the circle.
4) Using the Intersection tool, mark the intersection of circle D and line DE as G
6) Using the Compass tool, construct circle C with radius CF.
7) Bring circle F to ray DE making G the new center of the circle.
8) Using the Intersection tool, mark one intersection of your two circles on ray DE as point H
9) Using the Ray tool, construct a ray from point D through point H.
You have now constructed an angle congruent to angle ABC
Congruent Angle
Follow the same steps as above to construct an angle congruent to angle ABC
Congruent Angle
Follow the same steps as above to construct an angle congruent to angle ABC
Congruent Angle
Angle Bisector
1) Using the Circle through a point tool, construct Circle B such that it crosses ray BA and ray BC
2) Using the Intersection tool, mark the intersection of circle B and ray BA as D and the intersection of circle B and ray BC as E
3) Follow the same steps from the Midpoint/Perpendicular Bisector Tasks, construct the bisector of arc DE the same as you would a segment.
Angle Bisector
Follow the same steps as above to construct an angle bisector