1. Centroid 
The CENTROID(G) of a triangle is the common intersection of the three medians. 
2. Orthocenter 
The ORTHOCENTER(H) of a triangle is the common intersection of the three lines containig the altitudes. 
3. Circumcenter 
The CIRCUMCENTER(C) of a triangle is the point in the plane equidistant from the three vertices of the triangle. 
4. Circumcircle 
The CIRCUMCIRCLE of a triangle is a circumscribed circle that passes three vertices of the triangle, and its center is the circumcenter. 
5. Incenter 
The INCENTER(I) of a triangle is the point on the interior of the triangle that is equidistant from the three sides. 
6. Incircle 
The INCIRCLE of a triangle is a inscribed circle whose center is the incenter. 
7. Medial triangle 
The MEDIAL TRIANGLE is a triangle with vertices as the midpoints of the triangle. 
8. Orthocenter, Midsegment triangle 
The MIDSEGMENT TRIANGLE is a triangle that is formed by midsegments of a triangle, which are the line segments joining midpoints of two sides of a triangle. 
9. Orthic triangle 
The ORTHIC TRIANGLE is a triangle joining the feet of the altitudes of the triangle. 
10. Pedal triangle 
The PEDAL TRIANGLE is a triangle whose vertices are the feet of perpendiculars from each vertex of the triangle to their opposite sides in
the triangle. 
11. Center of Nine point circle 
The CENTER OF NINE POINT CIRCLE is the center of the nine point circle. 
12. Nine Point Circle

The NINE POINT CIRCLE is a circle that passes through nine significant points, six lying on the triangle itself (unless the triangle is obtuse). They include:
 The midpoint of each side of the triangle
 The foot of each altitude
 The midpoint of the segment of each altitude from its vertex to the orthocenter (where the three altitudes meet)

13. Trisecting a line segment 
This is how to draw TRISECTING points of a LINE SEGMENT. 
14. Equilateral triangle, given a side 
The EQUILATERAL TRIANGLE is a triangle that has three congruent sides.
 This is how to draw a EQUILATERAL TRIANGLE with GIVEN SIDE.

15. Square, given a side 
The SQUARE is a quadrilateral that has four congruent sides and four congruent angles.
 This is how to draw a SQUARE with GIVEN SIDE.

16. Isosceles triangle, given base and altitude 
The ISOSCELES TRIANGLE is a triangle that has two congruent sides. 
17. Triangle Centers (H, G, C, and I) 
The FOUR CENTERS OF TRIANGLES are ORTHOCENTER(H), CENTROID(G), CIRCUMCENTER(C), and INCENTER(I). 
18. Triangle Centers with Euler Line 
The EULER LINE of a triangle is a line that passes the Center of nine point circle, the Circumcenter(C), Centroid(G), and Orthocenter(H) of the triangle. 
19. Locus of vertex of a fixed angle that subtends a fixed segment

This is how to draw a LOCUS of the VERTEX of a FIXED ANGLE that SUBSTANDS a FIXED SEGMENT. 
20. Divide a segment AB into two parts that form a golden ratio

The GOLDEN RATIO, phi, is 0.6180339887...
 A GOLDEN RATIO of a LINE SEGMENT is the ratio that is the length of the larger portion of the line segment to the length of the whole line segment.

21. Pentagon, given a radius

The PENTAGON is a polygon that has five sides.
 This is how to draw a PENTAGON with GIVEN RADIUS.

22. Pentagon, given a side

The PENTAGON is a polygon that has five sides.
 This is how to draw a PENTAGON with GIVEN SIDE.

23. Hexagon, given a side

The HEXAGON is a polygon that has six sides.
 This is how to draw a HEXAGON with GIVEN SIDE.

24. Octagon, given a side

The OCTAGON is a polygon that has eight sides.
 This is how to draw a OCTAGON with GIVEN SIDE.
