Advanced Euclidean Geometry

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

$Math 3000 Running Glossary$

9-Points Circle Worksheet Angle JB'A' is thus a right angle and so, B' must be on the circle with diameter A'J. y) In an analogous manner, prove that C' is on the circle with diameter A'J. We therefore have J, A', B' and C' all on the same circle, which is the circle we started with. By repeating this argument starting with the circles having diameters KB' and LC', we can show that K and L are also on this circle.
9-point Circle Thm 4.17: The centroid of a triangle trisects the segment joining the circumcenter and the orthocenter. [Euler line] C A H A' O M B Draw circumcircle and extend radius CO to diameter COM. ΔCBM ~ ΔCA'O so OA' = ½MB Drop altitude from A, find orthocenter H. AMBH is a parallelogram, so AH = MB = 2OA'.
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 and 16: A Circle Theorem Thm 4.9: The produ
Page 17 and 18: Directed Segments The next few theo
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: 9-Points Circle Worksheet Since A'D
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

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