Spherical Geometry Activities - Notes
... on the sphere. How would you describe it? Why does the great circle correspond to a line on the plane?] The extensions will meet up with each other; put another way, if you go along a great circle then you will eventually return to your starting point. [The great circle is the largest circle that is ...
... on the sphere. How would you describe it? Why does the great circle correspond to a line on the plane?] The extensions will meet up with each other; put another way, if you go along a great circle then you will eventually return to your starting point. [The great circle is the largest circle that is ...
Reteaching
... The new angle is the sum of the angles that come together. Since 35 + 55 = 90, the pieces form right angles. Two lines that are perpendicular to the same line are parallel. So, each set of sides is parallel. ...
... The new angle is the sum of the angles that come together. Since 35 + 55 = 90, the pieces form right angles. Two lines that are perpendicular to the same line are parallel. So, each set of sides is parallel. ...
Axiomatic Systems/Fe
... means that AX, BY, and CZ are concurrent. These segments were defined as the medians of the triangle ABC. Thus, the three medians of a triangle are concurrent. 7) We are told that M is the midpoint of BC (which means segments BM and MC are congruent) and segments AM and AE are congruent. Since angle ...
... means that AX, BY, and CZ are concurrent. These segments were defined as the medians of the triangle ABC. Thus, the three medians of a triangle are concurrent. 7) We are told that M is the midpoint of BC (which means segments BM and MC are congruent) and segments AM and AE are congruent. Since angle ...
Geometry (H) Worksheet: 1st Semester Review:True/False, Always
... 40. Two lines perpendicular to the same line are parallel to each other. 41. Two lines parallel to the same line are parallel to each other. 42. Another name for an if-then statement is a conditional. 43. The converse of a conditional is formed by negating the hypothesis ad the conclusion. 44. The c ...
... 40. Two lines perpendicular to the same line are parallel to each other. 41. Two lines parallel to the same line are parallel to each other. 42. Another name for an if-then statement is a conditional. 43. The converse of a conditional is formed by negating the hypothesis ad the conclusion. 44. The c ...
Katie Hoppe - STMA Schools
... area of a prism and cylinder. LT 4 I can find the volume of a prism and cylinder. LT 5 I can find the surface area of a pyramid and cone. LT 6 I can find the volume of a pyramid and cone. LT 7 I can find the surface area of a sphere. LT 8 I can find the volume of a sphere. LT 9 I can use relationshi ...
... area of a prism and cylinder. LT 4 I can find the volume of a prism and cylinder. LT 5 I can find the surface area of a pyramid and cone. LT 6 I can find the volume of a pyramid and cone. LT 7 I can find the surface area of a sphere. LT 8 I can find the volume of a sphere. LT 9 I can use relationshi ...
Chapter 1 - South Henry School Corporation
... 4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is ...
... 4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is ...
Old and New Results in the Foundations of Elementary Plane
... For arbitrary Hilbert planes, the Circle-Circle axiom is equivalent to the Triangle Existence theorem [20, Corollary, p. 173] and implies the Line-Circle axiom [20, Major Exercise 1, p. 200]. Conversely, Strommer [43] proved that Line-Circle implies Circle-Circle in all Hilbert planes, first proving ...
... For arbitrary Hilbert planes, the Circle-Circle axiom is equivalent to the Triangle Existence theorem [20, Corollary, p. 173] and implies the Line-Circle axiom [20, Major Exercise 1, p. 200]. Conversely, Strommer [43] proved that Line-Circle implies Circle-Circle in all Hilbert planes, first proving ...
G.2 - DPS ARE
... when the conditions determine a unique triangle, more than one triangle, or no triangle. ...
... when the conditions determine a unique triangle, more than one triangle, or no triangle. ...
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 in a plane may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.