Advanced Euclidean Geometry

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

$Math 3000 Running Glossary$

The 9-Point Circle Worksheet We will start by recalling some high school geometry facts. 1. The line joining the midpoints of two sides of a triangle is parallel to the third side and measures 1/2 the length of the third side of the triangle. a) Why is the ratio of side AD to side AB 1:2? b) In the diagram, ΔDAE is similar to ΔBAC because .... Since similar triangles have congruent angles, we have that ∠ADE ≅ ∠ABC. c) Line DE is parallel to BC because .... d) Since the ratio of corresponding sides of similar triangles is constant, what is the ratio of side DE to side BC?
The 9-Point Circle Worksheet 2. Four points, forming the vertices of a quadrilateral, lie on a circle if and only if the sum of the opposite angles in the quadrilateral is 180 o . e) An angle inscribed in a circle has measure equal to 1/2 the measure of the arc it subtends. In the diagram above, what arc does the ∠DAB subtend? What arc does the opposite ∠BCD subtend? f) Since the total number of degrees of the arc of the full circle is 360 o , what is the sum of the measures of ∠DAB and ∠BCD?
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: Feuerbach's Circle Thm 4.16 : The m
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

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