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Unformatted text preview: it will be in the form of a problem - probably with hints. • In hyperbolic geometry o There are no rectangles o The angle defect is positive for all triangles o Similar triangles are congruent o The segment joining the midpoints of base and summit in a Saccheri quadrilateral makes right angles with the base and summit o Two Saccheri quadrilaterals are congruent if they have congruent summits and summit angles. • Construction of o Perpendicular from a point to a line o Segment and angle bisector o Tangent to a circle through a point outside the circle o Inverse of point through a circle o Orthogonal circles • An Isometry in Euclidean geometry: o Can always be constructed from at most 3 reflections o Is a rotation if it has exactly 1 fixed point, a reflection if it has 2 but not 3 non-collinear fixed points, and is the Identity if it has at least three non-collinear fixed points o Can be represented by a 3x3 matrix of the form given in Section 5.7.1...
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This note was uploaded on 08/08/2009 for the course MATH 1 taught by Professor Malkin during the Spring '09 term at University of Illinois at Urbana–Champaign.
- Spring '09