Spherical Geometry Homework
... out into the embedding space where you are. Start at point (1, 0, 0) and go around to (1, 0, 0). You’ve gone halfway around the equator and if you keep walking you’ll get all the way back to (1, 0, 0). You’ve gone a distance 2 with half of the coordinates positives and the other half negatives. Th ...
... out into the embedding space where you are. Start at point (1, 0, 0) and go around to (1, 0, 0). You’ve gone halfway around the equator and if you keep walking you’ll get all the way back to (1, 0, 0). You’ve gone a distance 2 with half of the coordinates positives and the other half negatives. Th ...
Chapter 5: Poincare Models of Hyperbolic Geometry
... −M followed by inversion in the unit circle. This map ϕ is an isometry because it is the composition of two isometries. Note that M is first sent to O and then to ∞ by inversion. Thus, the image of Γ is a (Euclidean) line. Since the center of the circle is on the real axis, the circle intersects the ...
... −M followed by inversion in the unit circle. This map ϕ is an isometry because it is the composition of two isometries. Note that M is first sent to O and then to ∞ by inversion. Thus, the image of Γ is a (Euclidean) line. Since the center of the circle is on the real axis, the circle intersects the ...
Regular Tesselations in the Euclidean Plane, on the
... both glide and mirror reflections symmetries. Note that in these illustrations the coloring has only aesthetical purposes. Figure 1 shows an example of a p4m-invariant tiling. A complete table of illustrations for the crystallographic groups can be found, for example, in [3]. The Fig.2. This is an e ...
... both glide and mirror reflections symmetries. Note that in these illustrations the coloring has only aesthetical purposes. Figure 1 shows an example of a p4m-invariant tiling. A complete table of illustrations for the crystallographic groups can be found, for example, in [3]. The Fig.2. This is an e ...
ASA and SAS Postulates - Clark Magnet High School
... In order to finish our “proof” investigation of the SAS postulate, we will do a reflection through line segment ED. If the two triangles are in fact congruent the C” should be able to map directly onto F because of this reflection. ...
... In order to finish our “proof” investigation of the SAS postulate, we will do a reflection through line segment ED. If the two triangles are in fact congruent the C” should be able to map directly onto F because of this reflection. ...
(Points, Lines, Planes and Transformations)
... Lines in the same plane that are always the same distance apart. They do not intersect. Skew lines Lines that are not in the same plane and do not intersect. Intersection The set of points that are in both figures. Concurrent lines Three or more lines that pass through the same point. Post ...
... Lines in the same plane that are always the same distance apart. They do not intersect. Skew lines Lines that are not in the same plane and do not intersect. Intersection The set of points that are in both figures. Concurrent lines Three or more lines that pass through the same point. Post ...
Document
... Many teachers and textbooks treat congruence as “same size, same shape”. This is not sufficient to transition from middle school to high school geometry. The key to grade specific rigor (informal to increased formalism) in CCSS is the transformational approach. Transformations (rigid motions + dilat ...
... Many teachers and textbooks treat congruence as “same size, same shape”. This is not sufficient to transition from middle school to high school geometry. The key to grade specific rigor (informal to increased formalism) in CCSS is the transformational approach. Transformations (rigid motions + dilat ...
A cyclic quadrilateral
... Given: Circle C with center C and radius r. Circle D with center D and radius s. Prove: Circle C is similar to circle D. To prove similarity, show that there is a sequence of similarity transformations that maps circle C to circle D. A) First, transform circle C with a ___________________ along vect ...
... Given: Circle C with center C and radius r. Circle D with center D and radius s. Prove: Circle C is similar to circle D. To prove similarity, show that there is a sequence of similarity transformations that maps circle C to circle D. A) First, transform circle C with a ___________________ along vect ...
Unit 5 GCO 6 - Using Rigid motions to show congruence - UCCA-2011
... Use the definition of congruence in terms of RIGID MOTIONS to decide if two figures are congruent. Develop Understanding Lesson Predict the effect of rotating, reflecting, or translating a given figure. Surface ideas such as: -sequences of transformations that will change the orientation of a shape ...
... Use the definition of congruence in terms of RIGID MOTIONS to decide if two figures are congruent. Develop Understanding Lesson Predict the effect of rotating, reflecting, or translating a given figure. Surface ideas such as: -sequences of transformations that will change the orientation of a shape ...
Activity 6.5.2 Cavalieri`s Principle and the Volume of a Sphere
... Activity 6.5.2 Cavalieri’s Principle and the Volume of a Sphere This is a more formal development of the formulas for the volume and surface area of a sphere. Consider a hemisphere with radius r and a cylinder with the same radius and height also equal to r. Inside the cylinder there is a cone with ...
... Activity 6.5.2 Cavalieri’s Principle and the Volume of a Sphere This is a more formal development of the formulas for the volume and surface area of a sphere. Consider a hemisphere with radius r and a cylinder with the same radius and height also equal to r. Inside the cylinder there is a cone with ...
GEOM_U4_BLM_Final
... 2. Put a + next to each word/phrase you know well and for which you can write an accurate example and definition. Your definition and example must relate to this unit of study. 3. Place a next to any words/phrases for which you can write either a definition or an example, but not both. 4. Put a – ...
... 2. Put a + next to each word/phrase you know well and for which you can write an accurate example and definition. Your definition and example must relate to this unit of study. 3. Place a next to any words/phrases for which you can write either a definition or an example, but not both. 4. Put a – ...