Advanced Euclidean Geometry

More documents

Recommendations

Info

$University of Colorado Denver Math 1070 Topics Updated: Fall 2009 ...$

$Math 3000 Running Glossary$

a b h c Area Formulas A = ½ bh Heron's formula for the area of a triangle. A= s s−a s−b s−c, where s= abc 2 the semiperimeter Brahmagupta's formula for the area of a cyclic quadrilateral. A= s−a s−b s−c s−d
Directed Segments The next few theorems involve the lengths of line segment and we want to permit directed lengths (positive and negative). By convention we assign to each line an independent direction. Each length measured in the same direction as the assigned one is positive and those in the opposite direction are negative. A B A B AB positive, BA negative AB negative, BA positive With this convention, internal ratios are always positive and external ratios are always negative. A C B A B C AC CB AC CB 0 0
Page 1 and 2: Advanced Euclidean Geometry
Page 3 and 4: Circumcenter Equally far from the v
Page 5 and 6: Examples: Circumcenter (O)
Page 7 and 8: Orthocenter (H) Thm 4.2: The altitu
Page 9 and 10: Equally far from the sides? A B C I
Page 11 and 12: Examples: Incenter (I)
Page 13 and 14: Internal Bisectors Thm 4.5: The int
Page 15: A Circle Theorem Thm 4.9: The produ
Page 19 and 20: I B' II A D E A' III B C Menelaus'
Page 21 and 22: Ceva's Theorem Thm 4.13 : Ceva's Th
Page 23 and 24: Ceva's Theorem Note that the text d
Page 25 and 26: Gergonne Point Thm 4.14: The lines
Page 27 and 28: Miquel Point Thm 4.19 : If three po
Page 29 and 30: Feuerbach's Circle Thm 4.16 : The m
Page 31 and 32: The 9-Point Circle Worksheet 2. Fou
Page 33 and 34: 9-Point Circle Worksheet A trapezoi
Page 35 and 36: 9-Points Circle Worksheet 4. In a r
Page 37 and 38: 9-Points Circle Worksheet Since A'D
Page 39 and 40: 9-point Circle Thm 4.17: The centro
Page 41 and 42: 9-point Circle Thm 4.18: The center
Page 43 and 44: Symmedian In a triangle, lines thro
Page 45 and 46: c b B a C Law of Sines A a sin A =
Page 47 and 48: Theorem Theorem: The isogonal conju
Page 49 and 50: Morley's Theorem The incenter I of
Page 51 and 52: Draw the sides of ΔABC and note th

Advanced Euclidean Geometry

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?