Slides for Nov. 12, 2014, lecture
... needs three spatial lengths (coordinates, say, in a fixed coordinate system) to fix one of its points; manifold a collection of points or elements (objects, entities) that has the structure of a multiply extended magnitude, i.e., has a fixed number of associated modes of specification of magnitude-c ...
... needs three spatial lengths (coordinates, say, in a fixed coordinate system) to fix one of its points; manifold a collection of points or elements (objects, entities) that has the structure of a multiply extended magnitude, i.e., has a fixed number of associated modes of specification of magnitude-c ...
2.6 Special Angles on Parallel Lines powerpoint
... Are the two sets of angles congruent? Slide the top copy so that the transversal stays lined up. Trace the lines and the angles from your paper onto the patty paper. 6. What kinds of angles were formed? 7. Use your ruler to measure the distance between the two lines in three different places. Are th ...
... Are the two sets of angles congruent? Slide the top copy so that the transversal stays lined up. Trace the lines and the angles from your paper onto the patty paper. 6. What kinds of angles were formed? 7. Use your ruler to measure the distance between the two lines in three different places. Are th ...
Slide 1
... 3-3 Proving Lines Parallel Ms. Anderson’s Rowing Example # 1 During a race, all members of a rowing team should keep the oars parallel on each side. If on the port side m < 1 = (3x + 13)°, m<2 = (5x - 5)°, & x = 9. Show that the oars are parallel. ...
... 3-3 Proving Lines Parallel Ms. Anderson’s Rowing Example # 1 During a race, all members of a rowing team should keep the oars parallel on each side. If on the port side m < 1 = (3x + 13)°, m<2 = (5x - 5)°, & x = 9. Show that the oars are parallel. ...
Document
... 10 ft from his television set. Can the other two distances shown be 8 ft and 6 ft? Explain. Yes; the sum of any two lengths is greater than the third length. Holt Geometry ...
... 10 ft from his television set. Can the other two distances shown be 8 ft and 6 ft? Explain. Yes; the sum of any two lengths is greater than the third length. Holt Geometry ...
documentation dates
... Weeks 6-8 – Continues on next page Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1] Make formal geometric constructions with a variety of to ...
... Weeks 6-8 – Continues on next page Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment based on the undefined notions of point, line, distance along a line, and distance around a circular arc. [G-CO1] Make formal geometric constructions with a variety of to ...
2.6 Special Angles on Parallel Lines .pptx
... Are the two sets of angles congruent? Slide the top copy so that the transversal stays lined up. Trace the lines and the angles from your paper onto the patty paper. 6. What kinds of angles were formed? 7. Use your ruler to measure the distance between the two lines in three different places. Are ...
... Are the two sets of angles congruent? Slide the top copy so that the transversal stays lined up. Trace the lines and the angles from your paper onto the patty paper. 6. What kinds of angles were formed? 7. Use your ruler to measure the distance between the two lines in three different places. Are ...
number of sides
... A polygon with four sides. Each line is the same not more. Each angle is right. Can you guess with all your might? Now you know what is polygon, see if you can apply the knowledge: ...
... A polygon with four sides. Each line is the same not more. Each angle is right. Can you guess with all your might? Now you know what is polygon, see if you can apply the knowledge: ...
GEOMETRIC SEARCHING PART 1: POINT LOCATION
... = Ax By + BxCy + Cx Ay - Ax Cy - BxAy - Cx By Počítáme orientation jako sign(2T) nebo ...
... = Ax By + BxCy + Cx Ay - Ax Cy - BxAy - Cx By Počítáme orientation jako sign(2T) nebo ...
6-3 - Spring Branch ISD
... using the definition of parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0). ...
... using the definition of parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0). ...
Document
... 5-5 in One Triangle Check It Out! Example 1 Write an indirect proof that a triangle cannot have two right angles. Step 1 Identify the conjecture to be proven. Given: A triangle’s interior angles add up to 180°. Prove: A triangle cannot have two right angles. Step 2 Assume the opposite of the conclus ...
... 5-5 in One Triangle Check It Out! Example 1 Write an indirect proof that a triangle cannot have two right angles. Step 1 Identify the conjecture to be proven. Given: A triangle’s interior angles add up to 180°. Prove: A triangle cannot have two right angles. Step 2 Assume the opposite of the conclus ...
M/J Mathematics 1 2002050
... Throughout the year, students will relate new vocabulary to familiar words, listen to, read, and discuss familiar and conceptually challenging text and will use new vocabulary that is introduced and taught directly. (LA.910.1.6.1, 6.2, 6.5 and LA.1112.1.6.1, 6.2, 6.5) Students will also use a variet ...
... Throughout the year, students will relate new vocabulary to familiar words, listen to, read, and discuss familiar and conceptually challenging text and will use new vocabulary that is introduced and taught directly. (LA.910.1.6.1, 6.2, 6.5 and LA.1112.1.6.1, 6.2, 6.5) Students will also use a variet ...
On Lobachevsky`s trigonometric formulae
... one has to consider only spherical triangles contained in a hemisphere, in order to avoid pairs of points which can be joined by two distinct segments.) Distances and angles on this geometric sphere are also defined in analogy with those of spherical triangles on a standard sphere embedded in Euclid ...
... one has to consider only spherical triangles contained in a hemisphere, in order to avoid pairs of points which can be joined by two distinct segments.) Distances and angles on this geometric sphere are also defined in analogy with those of spherical triangles on a standard sphere embedded in Euclid ...
Toolbox - Ephrata School
... 7-2 Ratios in Similar Polygons Example 1: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. ∠N ≅ ∠Q and ∠P ≅ ∠R. By the Third Angles Theorem, ∠M ≅ ∠T. ...
... 7-2 Ratios in Similar Polygons Example 1: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. ∠N ≅ ∠Q and ∠P ≅ ∠R. By the Third Angles Theorem, ∠M ≅ ∠T. ...
Powerpoint 3.2
... 1. m1 = 120°, m2 = (60x)° Alt. Ext. s Thm.; m2 = 120° 2. m2 = (75x – 30)°, m3 = (30x + 60)° Corr. s Post.; m2 = 120°, m3 = 120° 3. m3 = (50x + 20)°, m4= (100x – 80)° Alt. Int. s Thm.; m3 = 120°, m4 =120° 4. m3 = (45x + 30)°, m5 = (25x + 10)° Same-Side Int. s Thm.; m3 = 120°, m5 =6 ...
... 1. m1 = 120°, m2 = (60x)° Alt. Ext. s Thm.; m2 = 120° 2. m2 = (75x – 30)°, m3 = (30x + 60)° Corr. s Post.; m2 = 120°, m3 = 120° 3. m3 = (50x + 20)°, m4= (100x – 80)° Alt. Int. s Thm.; m3 = 120°, m4 =120° 4. m3 = (45x + 30)°, m5 = (25x + 10)° Same-Side Int. s Thm.; m3 = 120°, m5 =6 ...
Tessellations: The Link Between Math and Art
... There are similarities between Euclidean, hyperbolic and elliptic geometries. In the study of isometries, we see Euclidean analogs of the transformations in both the hyperbolic and elliptic plane. Isometries can be expressed as the composition of reflections in all three planes. Many similarities ex ...
... There are similarities between Euclidean, hyperbolic and elliptic geometries. In the study of isometries, we see Euclidean analogs of the transformations in both the hyperbolic and elliptic plane. Isometries can be expressed as the composition of reflections in all three planes. Many similarities ex ...
7.2 Lesson
... 7-2 Ratios in Similar Polygons Warm Up 1. If ∆QRS ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Q Z; R Y; S X; QR ZY; RS YX; QS ZX Solve each proportion. ...
... 7-2 Ratios in Similar Polygons Warm Up 1. If ∆QRS ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Q Z; R Y; S X; QR ZY; RS YX; QS ZX Solve each proportion. ...
Triangles in Hyperbolic Geometry
... see how they relate to each other and to orthogonal circles. Radical Axis 1. The locus of points whose power with respect to two non-concentric circles are equal is a line perpendicular to the line of centers of the two circles. That line is the radical axis and contains the common chord of the two ...
... see how they relate to each other and to orthogonal circles. Radical Axis 1. The locus of points whose power with respect to two non-concentric circles are equal is a line perpendicular to the line of centers of the two circles. That line is the radical axis and contains the common chord of the two ...
Geometry CSO - Fayette County Schools
... compare and contrast Euclidean geometry to other geometries (i.e. spherical, elliptic) using various forms of communication such as development of physical models, oral or written reports. M.O.G.3.21 approximate the area of irregularly shaped regions based on the approximations and the attributes of ...
... compare and contrast Euclidean geometry to other geometries (i.e. spherical, elliptic) using various forms of communication such as development of physical models, oral or written reports. M.O.G.3.21 approximate the area of irregularly shaped regions based on the approximations and the attributes of ...
8-1 Similar polygons
... Ratios in Similar Polygons Check It Out! Example 3 A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch. ...
... Ratios in Similar Polygons Check It Out! Example 3 A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch. ...
Congruent Triangles
... AC is the non-included side in relation to angles B and C. AB is the non-included side in relation to angles B and C. homework Holt Geometry ...
... AC is the non-included side in relation to angles B and C. AB is the non-included side in relation to angles B and C. homework Holt Geometry ...
Angles Formed by Parallel Lines and Transversals
... 1. m1 = 120°, m2 = (60x)° Alt. Ext. s Thm.; m2 = 120° 2. m2 = (75x – 30)°, m3 = (30x + 60)° Corr. s Post.; m2 = 120°, m3 = 120° 3. m3 = (50x + 20)°, m4= (100x – 80)° Alt. Int. s Thm.; m3 = 120°, m4 =120° 4. m3 = (45x + 30)°, m5 = (25x + 10)° Same-Side Int. s Thm.; m3 = 120°, m5 =6 ...
... 1. m1 = 120°, m2 = (60x)° Alt. Ext. s Thm.; m2 = 120° 2. m2 = (75x – 30)°, m3 = (30x + 60)° Corr. s Post.; m2 = 120°, m3 = 120° 3. m3 = (50x + 20)°, m4= (100x – 80)° Alt. Int. s Thm.; m3 = 120°, m4 =120° 4. m3 = (45x + 30)°, m5 = (25x + 10)° Same-Side Int. s Thm.; m3 = 120°, m5 =6 ...
Shape of the universe
The shape of the universe is the local and global geometry of the Universe, in terms of both curvature and topology (though, strictly speaking, the concept goes beyond both). The shape of the universe is related to general relativity which describes how spacetime is curved and bent by mass and energy.There is a distinction between the observable universe and the global universe. The observable universe consists of the part of the universe that can, in principle, be observed due to the finite speed of light and the age of the universe. The observable universe is understood as a sphere around the Earth extending 93 billion light years (8.8 *1026 meters) and would be similar at any observing point (assuming the universe is indeed isotropic, as it appears to be from our vantage point).According to the book Our Mathematical Universe, the shape of the global universe can be explained with three categories: Finite or infinite Flat (no curvature), open (negative curvature) or closed (positive curvature) Connectivity, how the universe is put together, i.e., simply connected space or multiply connected.There are certain logical connections among these properties. For example, a universe with positive curvature is necessarily finite. Although it is usually assumed in the literature that a flat or negatively curved universe is infinite, this need not be the case if the topology is not the trivial one.The exact shape is still a matter of debate in physical cosmology, but experimental data from various, independent sources (WMAP, BOOMERanG and Planck for example) confirm that the observable universe is flat with only a 0.4% margin of error. Theorists have been trying to construct a formal mathematical model of the shape of the universe. In formal terms, this is a 3-manifold model corresponding to the spatial section (in comoving coordinates) of the 4-dimensional space-time of the universe. The model most theorists currently use is the so-called Friedmann–Lemaître–Robertson–Walker (FLRW) model. Arguments have been put forward that the observational data best fit with the conclusion that the shape of the global universe is infinite and flat, but the data are also consistent with other possible shapes, such as the so-called Poincaré dodecahedral space and the Picard horn.