# ORTHIC TRIANGLE

The triangle joining the feet of the altitudes of a triangle is called the orthic triangle.

# PEDAL TRIANGLE

The pedal triangle is the triangle whose vertices are the feet of the perpendiculars from the point to the sides of the given triangle.

# NINE POINT CIRCLE

It is a circle that passes through nine significant concyclic points defined from the triangle

# CENTER OF THE NINE POINT CIRCLE

The center of the circle defined above

# TRISECTING A LINE SEGMENT

Dividing a segment into three equal parts

# EQUILATERAL TRIANGLE GIVEN ONE SIDE

Equilateral triangles have equal sides and angles. Here one is constructed given one side.

# SQUARE GIVEN A SIDE

Four equal sides and four ninety degree angles define a square. Here one is constructed given a side.

# ISOSCELES TRIANGLE GIVEN BASE AND ALTITUDE

Isosceles triangles have two equal sides and two equal angles. Here one is constructed given a base and altitude

# TRIANGLE CENTERS

Orthocenter, Centroid, Circumcenter and Incenter

# TRIANGLE CENTERS WITH EULER LINES

It is a line that passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, and the center of the nine-point circle of the triangle.

# LOCUS VERTEX OF A FIXED ANGLE SUBTENDING A FIXED VERTEX

Here one is constructed

# DIVIDE A SEGMENT AB INTO TWO PARTS THAT FORM A GOLDEN RATION

Here one is constructed

A polygon with five sides and five angles. Here one is constructed given a radius

# PENTAGON GIVEN A SIDE

A polygon with five sides and five angles. Here one is constructed given a side

# HEXAGON GIVEN A SIDE

A polygon with six sides and six angles. Here one is drawn given a side

# OCTAGON GIVEN A SIDE

A polygon with eight sides and eight angles. Here one is drawn given a side