*by Soo Jin
Lee*

1. Centroid

2. Orthocenter

3. Circumcenter

4. Circumcircle

5. Incenter

6. Incircle

*the triangle formed by joining the midpoints
of the sides of a triangle*

8. Orthocenter, Mid-segment triangle;

*a Mid-Segment Triangle is a triangle created
from a larger triangle. Once the orthocenter on the larger triangle
is constructed, the mid-segment triangle uses the midpoint of
each vertex to the orthocenter as the vertices.*

9. Orthic triangle;

*an Orthic Triangle is similar to a medial
triangle, but uses the intersection points of the altitudes of
the larger triangle as its vertices.*

10. Pedal triangle;

*the pedal triangle of P is the triangle
whose polygon vertices are the feet of the perpendiculars from
P to the side lines.*

11. Center of Nine point circle;

*the nine-point circle, also called Euler's
circle or the Feuerbach circle, is the circle that passes through
the feet of the perpendicular , , and dropped from the vertices
of any triangle on the sides opposite them.*

*the nine-point circle, also called Euler's
circle or the Feuerbach circle, is the circle that passes through
the feet of the perpendicular , , and dropped from the vertices
of any triangle on the sides opposite them.*

If you click thrisectiong line segmetn, you can see the segment AB is trisected by two points D, E.

14. Equilateral triangle, given a side

16. Isosceles triangle, given base and altitude

17. Triangle Centers

18. Triangle Centers with Euler Line;

*The line on which the orthocenter, triangle
centroid, circumcenter, nine-point center, and number of other
important triangle centers lie.*

19. Locus of vertex of a fixed angle that subtends a fixed segment.

20. Divide a segment AB into two parts that form a golden ratio.