Stephanie K. Lewis
7. Medial triangle
7a. Orthocenter, Mid-segment triangle
8. Orthic triangle
9. Pedal triangle
A triangle inscribed in
a given triangle in the following
manner: its vertices are the feet
of the three perpendiculars to
the sides from some point
inside the given triangle.
10. Center of Nine-point circle
11. Nine Point Circle
12. Trisecting a line segment
13. Equilateral triangle, given a side
Equiangular triangles are also equilateral.
14. Square, given a side
Note: Each angle is 90° , and all sides are equal.
15. Isosceles triangle, given base and altitude
16. Triangle Centers (H, G, C, and I)
Triangle Center H, the Orthocenter, is the point at which the three lines containing the altitudes intersect. This sketch can be observed by looking at A5#2.
Triangle Center G, the Centroid, is the common intersection of the three medians. This sketch can be observed by looking at A5#1.
Triangle Center C, the Circumcenter, is the point in the plane equidistant from the three vertices of the triangle. This sketch can be observed by looking at A5#3.
Triangle Center I, the Incenter, is the point on the interior of the triangle that is equidistant from the three sides. This sketch can be observed by looking at A5#5.
17. Triangle Centers with Euler Line
18. Locus of vertex of a fixed angle that subtends a fixed segment
19. Divide a segment AB into two parts that form a golden ratio.
20. Pentagon, given a radius.
21. Pentagon, given a side.
22. Hexagon, given a side.
23. Octagon, given a side.