A brief libraray of some useful definitions, diagrams, and constructions

Allyson Hallman

 

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Explorations with Sine and Cosine 

 

 

Varying Coefficients of Quadratic Equations 

 

 

Locus of Vertices of Parabolas 

 

 

Explorations of Triangle Circumcenters 

  

 

Fun with Medians of Triangles 

 

 

Tangent Circles 

 

 

Orthocenters and Circumcenters, oh my! 

 

 

Similiarity of Pedal Traingles

 

 

Parametric Equations 

 

 

Flower Power Polar Equations

 

 

Hiding the Biggest Box

 

 

Ceva’s Theorem

 

 

Bouncing Barney  

 

 

 

Concurrent Lines & Point of Concurrency

 

 

 

Concurrent lines intersect in a single point and that point of intersection is the point of concurrency

 

Centroid

 

 

 

Point of concurrency of medians of a triangle

 

 

 

Incenter

 

 

 

Point of concurrency of angle bisectors of a triangle

Circumcenter

 

 

 

Point of concurrency of perpendicular bisectors of sides of a triangle

Orthocenter

 

 

 

Point of concurrency of the altitudes of a triangle

Circumcircle

 

 

 

Circle whose center is the point of concurrency of the perpendicular bisectors of the sides or a triangle and whose radius is the distance from that point to any vertex of the triangle

 

Incircle

 

 

 

Circle whose center is the point of concurrency of angle bisectors of a triangle and whose radius is the distance from that point to any side of the triangle.

Triangle Centers

 

 

 

C = Circumcenter

I = Incenter

H = Orthocenter

G = Centroid

Triangle Centers with Euler Line

 

 

Line containing circumcenter, orthocenter, and centroid

Medial Triangle

 

 

Triangle whose vertices are the midpoints of the sides of another triangle

Orthic Triangle

 

 

Triangle whose vertices are the feet of the altitudes of another triangle

 

 

*feet?? Click here.

Pedal Triangle

 

Triangle whose vertices are the feet of the perpendiculars from any point P to each side of the triangle

 

Orthocenter, Midsegment Triangle

 

 

Triangle whose vertices are the midpoints of the segments connecting the orthocenter to each vertex

Nine Point Circle

 

 

Circle that passes through the midpoints of each side of a triangle (Ma, Mb, Mc), feet of the altitudes of that triangle (Ha, Hb, Hc), and the midpoints of the segments that connect the vertices of that triangle to its orthocenter (Oa, Ob, Oc)

Equilateral Triangle

 

 

Triangle with all three sides congruent

Isosceles Triangle

 

 

Triangle with at least two sides congruent

Square

 

 

 

Quadrilateral with four congruent sides and 4 congruent angles

Regular Pentagon

(given radius or side)

 

 

Polygon with five congruent sides

       

Regular Hexagon

(given side)

 

 

Polygon with six congruent sides

Regular Octagon

(given side)

 

 

Polygon with eight congruent sides

Golden Ratio

 

 

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

 

Trisect a segment

 

 

Divide a segment into three congruent parts