Chapter 13 One-Pagers — The Concurrence Theorems

One page per lesson, based on the teaching plan’s terms, theorems, and constructions. Each page gives the vocabulary, the key ideas, a homework helper, and common mistakes.

Lesson	Topic	One-pager
1	Triangles and Circles	Lesson 1
2	Cyclic Quadrilaterals	Lesson 2
3	Incircles	Lesson 3
4	The Centroid of a Triangle	Lesson 4
5	Ceva’s Theorem	Lesson 5
6	Napoleon’s Discovery and Other Surprises	Lesson 6

Theorem map

Result	Statement
Theorem 68	Every triangle is cyclic.
Corollary 68	The perpendicular bisectors of a triangle’s sides are concurrent.
Theorem 69	A quadrilateral is cyclic iff a pair of opposite angles are supplementary.
Theorem 70	Every triangle has an incircle.
Corollary 70	The angle bisectors of a triangle are concurrent.
Theorem 71	The medians of a triangle are concurrent.
Theorem 72	The lines containing the altitudes of a triangle are concurrent.
Theorem 73	Ceva’s Theorem: three cevians are concurrent iff (AX/XB)(BY/YC)(CZ/ZA) = 1.