1. Step-by-Step Constructions Perpendicular Through A Point (off a line) Equilateral Triangle What’s Wrong with SSA? Circumcenter Incenter Centroid Perpendicular Bisector [click on a construction]

2. [return to start page] Use arrow keys to navigate slides or click here to advance Perpendicular Bisector

3. [return to start page] Use arrow keys to navigate slides or click here to advance 1.adjust compass setting so that it is over half the length of given segment 2.construct an arc from each endpoint of the segment, P 1 and P 2, (arcs must intersect one another twice) 3.connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector). The point where this perpendicular bisector intersects the original segment, C, is the midpoint Perpendicular Bisector

4. [return to start page] Use arrow keys to navigate slides or click here to advance 1.adjust compass setting so that it is over half the length of given segment 2.construct an arc from each endpoint of the segment, P 1 and P 2, (arcs must intersect one another twice) 3.connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector). The point where this perpendicular bisector intersects the original segment, C, is the midpoint Perpendicular Bisector

5. [return to start page] Use arrow keys to navigate slides or click here to advance 1.adjust compass setting so that it is over half the length of given segment 2.construct an arc from each endpoint of the segment, P 1 and P 2, (arcs must intersect one another twice) 3.connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector). The point where this perpendicular bisector intersects the original segment, C, is the midpoint Perpendicular Bisector

6. [return to start page] Use arrow keys to navigate slides or click here to advance 1.adjust compass setting so that it is over half the length of given segment 2.construct an arc from each endpoint of the segment, P 1 and P 2, (arcs must intersect one another twice) 3.connect the 2 points where the arcs intersect, A and B (this segment, AB, is the perpendicular bisector). The point where this perpendicular bisector intersects the original segment, C, is the midpoint Perpendicular Bisector

7. [return to start page] Use arrow keys to navigate slides or click here to advance Perpendicular Through A Point (off the line)

8. [return to start page] Use arrow keys to navigate slides or click here to advance Perpendicular Through a Point 1.adjust compass setting so that it is slightly more than the distance from the given point, P 1, to the line 2.place the compass point on P 1 and construct an arc that intersects the line in 2 places, P 2 and P 3 (if there's not enough room, you may need to extend the original line segment) 3.place the compass point on P 2 and construct an arc on the opposite side of the segment from the given point, P 1 4.repeat step #3 from other arc-line intersection, P 3 5.connect the original point, P 1, to the point where these two new arcs intersect, A, to create your perpendicular

9. [return to start page] Use arrow keys to navigate slides or click here to advance Perpendicular Through a Point 1.adjust compass setting so that it is slightly more than the distance from the given point, P 1, to the line 2.place the compass point on P 1 and construct an arc that intersects the line in 2 places, P 2 and P 3 (if there's not enough room, you may need to extend the original line segment) 3.place the compass point on P 2 and construct an arc on the opposite side of the segment from the given point, P 1 4.repeat step #3 from other arc-line intersection, P 3 5.connect the original point, P 1, to the point where these two new arcs intersect, A, to create your perpendicular

10. [return to start page] Use arrow keys to navigate slides or click here to advance Perpendicular Through a Point 1.adjust compass setting so that it is slightly more than the distance from the given point, P 1, to the line 2.place the compass point on P 1 and construct an arc that intersects the line in 2 places, P 2 and P 3 (if there's not enough room, you may need to extend the original line segment) 3.place the compass point on P 2 and construct an arc on the opposite side of the segment from the given point, P 1 4.repeat step #3 from other arc-line intersection, P 3 5.connect the original point, P 1, to the point where these two new arcs intersect, A, to create your perpendicular

11. [return to start page] Use arrow keys to navigate slides or click here to advance Perpendicular Through a Point 1.adjust compass setting so that it is slightly more than the distance from the given point, P 1, to the line 2.place the compass point on P 1 and construct an arc that intersects the line in 2 places, P 2 and P 3 (if there's not enough room, you may need to extend the original line segment) 3.place the compass point on P 2 and construct an arc on the opposite side of the segment from the given point, P 1 4.repeat step #3 from other arc-line intersection, P 3 5.connect the original point, P 1, to the point where these two new arcs intersect, A, to create your perpendicular

12. [return to start page] Use arrow keys to navigate slides or click here to advance Perpendicular Through a Point 1.adjust compass setting so that it is slightly more than the distance from the given point, P 1, to the line 2.place the compass point on P 1 and construct an arc that intersects the line in 2 places, P 2 and P 3 (if there's not enough room, you may need to extend the original line segment) 3.place the compass point on P 2 and construct an arc on the opposite side of the segment from the given point, P 1 4.repeat step #3 from other arc-line intersection, P 3 5.connect the original point, P 1, to the point where these two new arcs intersect, A, to create your perpendicular

13. [return to start page] Use arrow keys to navigate slides or click here to advance Equilateral Triangle

14. [return to start page] Use arrow keys to navigate slides or click here to advance Equilateral Triangle 1.construct a segment 2.place the compass tip on one endpoint, P 1, and adjust the pencil so that it reaches the other endpoint, P 2. Construct an arc above the segment (using the length of the segment as the measure of your compass) 3.repeat step #2 from the other endpoint, P 2 (keeping the compass measure the same) to locate A 4.connect the point where these two arcs intersect, A, to create an equilateral triangle

15. [return to start page] Use arrow keys to navigate slides or click here to advance Equilateral Triangle 1.construct a segment 2.place the compass tip on one endpoint, P 1, and adjust the pencil so that it reaches the other endpoint, P 2. Construct an arc above the segment (using the length of the segment as the measure of your compass) 3.repeat step #2 from the other endpoint, P 2 (keeping the compass measure the same) to locate A 4.connect the point where these two arcs intersect, A, to create an equilateral triangle

16. [return to start page] Use arrow keys to navigate slides or click here to advance Equilateral Triangle 1.construct a segment 2.place the compass tip on one endpoint, P 1, and adjust the pencil so that it reaches the other endpoint, P 2. Construct an arc above the segment (using the length of the segment as the measure of your compass) 3.repeat step #2 from the other endpoint, P 2 (keeping the compass measure the same) to locate A 4.connect the point where these two arcs intersect, A, to create an equilateral triangle

17. [return to start page] Use arrow keys to navigate slides or click here to advance Equilateral Triangle 1.construct a segment 2.place the compass tip on one endpoint, P 1, and adjust the pencil so that it reaches the other endpoint, P 2. Construct an arc above the segment (using the length of the segment as the measure of your compass) 3.repeat step #2 from the other endpoint, P 2 (keeping the compass measure the same) to locate A 4.connect the point where these two arcs intersect, A, to create an equilateral triangle

18. [return to start page] Use arrow keys to navigate slides or click here to advance What’s Wrong with SSA?

19. [return to start page] Use arrow keys to navigate slides or click here to advance What’s Wrong with SSA? 1.duplicate one angle at P 1 2.duplicate one side, P 1 B 3.duplicate the next consecutive side, BA note, there are two possible intersections for the duplicated triangle P 1 BA 1or2 Original Triangle Duplication

20. [return to start page] Use arrow keys to navigate slides or click here to advance What’s Wrong with SSA? 1.duplicate one angle at P 1 2.duplicate one side, P 1 B 3.duplicate the next consecutive side, BA note, there are two possible intersections for the duplicated triangle P 1 BA 1or2 Original Triangle Duplication

21. [return to start page] Use arrow keys to navigate slides or click here to advance What’s Wrong with SSA? 1.duplicate one angle at P 1 2.duplicate one side, P 1 B 3.duplicate the next consecutive side, BA note, there are two possible intersections for the duplicated triangle P 1 BA 1or2 Original Triangle Duplication

22. [return to start page] Use arrow keys to navigate slides or click here to advance What’s Wrong with SSA? 1.duplicate one angle at P 1 2.duplicate one side, P 1 B 3.duplicate the next consecutive side, BA note, there are two possible intersections for the duplicated triangle P 1 BA 1or2

23. [return to start page] Use arrow keys to navigate slides or click here to advance Circumcenter

24. [return to start page] Use arrow keys to navigate slides or click here to advance Circumcenter 1.construct at least two perpendicular bisectors of the sides of a triangle (the intersection of the perpendicular bisectors, P 4, is the circumcenter) 2.place the compass tip on the circumcenter, P 4, and adjust the compass to a vertex, P 1 (this is the radius of the circumscribed circle), then construct the circumscribed circle

25. [return to start page] Use arrow keys to navigate slides or click here to advance Circumcenter 1.construct at least two perpendicular bisectors of the sides of a triangle (the intersection of the perpendicular bisectors, P 4, is the circumcenter) 2.place the compass tip on the circumcenter, P 4, and adjust the compass to a vertex, P 1 (this is the radius of the circumscribed circle), then construct the circumscribed circle

26. [return to start page] Use arrow keys to navigate slides or click here to advance Circumcenter 1.construct at least two perpendicular bisectors of the sides of a triangle (the intersection of the perpendicular bisectors, P 4, is the circumcenter) 2.place the compass tip on the circumcenter, P 4, and adjust the compass to a vertex, P 1 (this is the radius of the circumscribed circle), then construct the circumscribed circle

27. [return to start page] Use arrow keys to navigate slides or click here to advance Incenter

28. [return to start page] Use arrow keys to navigate slides or click here to advance Incenter 1.construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P 4, is the incenter) 2.from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle) 3.place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

29. [return to start page] Use arrow keys to navigate slides or click here to advance Incenter 1.construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P 4, is the incenter) 2.from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle) 3.place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

30. [return to start page] Use arrow keys to navigate slides or click here to advance Incenter 1.construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P 4, is the incenter) 2.from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle) 3.place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

31. [return to start page] Use arrow keys to navigate slides or click here to advance Incenter 1.construct at least two angle bisectors of the triangle (the intersection of the angle bisectors, P 4, is the incenter) 2.from the incenter, construct a perpendicular to any side of the triangle (this is the radius of the inscribed circle) 3.place the compass tip on the incenter and adjust the compass to the measure of the perpendicular from step #2, then construct the inscribed circle

32. [return to start page] Use arrow keys to navigate slides or click here to advance Centroid

33. [return to start page] Use arrow keys to navigate slides or click here to advance Centroid 1.construct at least two perpendicular bisectors of the triangle, label the midpoints A and B 2.connect each midpoint, A and B, to its opposite vertex, P 3 and P 2 to form medians AP 3 and BP 2. The point of intersection of these two medians is the centroid, C

34. [return to start page] Use arrow keys to navigate slides or click here to advance Centroid 1.construct at least two perpendicular bisectors of the triangle, label the midpoints A and B 2.connect each midpoint, A and B, to its opposite vertex, P 3 and P 2 to form medians AP 3 and BP 2. The point of intersection of these two medians is the centroid, C

35. [return to start page] Use arrow keys to navigate slides or click here to advance Centroid 1.construct at least two perpendicular bisectors of the triangle, label the midpoints A and B 2.connect each midpoint, A and B, to its opposite vertex, P 3 and P 2 to form medians AP 3 and BP 2. The point of intersection of these two medians is the centroid, C