Triangles: Theorems and Problems 39




Mittenpunkt Point
Triangle center 

Problem
1.
Triangle, median, angles, 45 degrees. 

Problem
2.
Triangle, angles, 10, 20 , 30 , 80 degrees. 

Problem
3.
Triangle, Angles, 45 degrees, Auxiliary Lines. 

Problem
5.
Triangle, cevian, equal segments, angles, cevian. 

Problem
6.
Triangle, cevian, equal segments, and angles. 

Problem
7.
Triangle, cevian, congruence, and angles. 

Problem
8.
Triangles, equal segments, angles, 45 degrees. 

Problem
9.
Triangles, equal segments, angles, 30 degrees. 

Problem
10.
Triangle, cevian, equal segments, angles, 8020 degrees. 

Equilic Quadrilateral.
Equilateral triangles. 

Nagel Point
Theorem. Proof.
Triangle center. 

Puzzle of
the Nagel Point: 22 pieces of polygons. 

Semiperimeter and excircles of a triangle.


Semiperimeter and incircle of a triangle. 

Semiperimeter, incircle and excircles of a triangle.


Gergonne Point Theorem.
Concurrency.
Interactive proof with animation.
Key concept: Ceva's
Theorem.


Ceva's Theorem.
Triangle, Concurrency.
Interactive proof with animation. Key concept:
Menelaus Theorem.


Puzzle of
the Ceva's Theorem: 48 classic piece. 

Menelaus' Theorem.
Interactive proof with animation and key concepts. 