Triangle and Holt Geometry Copyright

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• Hyperbolic Geometry and Omega Triangles Research Paper

  ...HYPERBOLIC GEOMETRY AND OMEGA TRIANGLES Hyperbolic geometry was first discovered and explored by Omar Khayyam in the 9th century and Giovanni Gerolamo Saccheri in the 15th century. Both were attempting to prove Euclid’s parallel postulate by proving the concept of hyperbolic geometry to be inconsistent, and ironically they discovered it to be a new type of geometry. It wasn’t until the 19th century that it became fully developed with help from Karl Friedrich Gauss, Janos Bolyai, and Nikolai Ivanovich Labachevsky. Later on, Eugenio Beltrami developed models of it and used these to prove that hyperbolic geometry is consistent if Euclidean geometry is. Hyperbolic geometry is a form of non-Euclidean geometry. It upholds all of Euclid’s principles except the parallel postulate that says that if given a line [pic]and a point[pic] not on [pic], there is exactly one line through[pic] that doesn’t intersect [pic]. Hyperbolic geometry instead has the following modified postulate: “given any line [pic], and point[pic]not on [pic], there are exactly two lines through[pic]which are hyperparallel to [pic], and an infinite number of lines through[pic]ultraparallel to [pic]” (Wikipedia). Hyperbolic geometry has become well-understood in two dimensions; however, not much is known about it in three dimensions except that it...

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• Geometry Essay

  ...Geometry Assignment Date: 24 June 2013 A. Name each of the following. Refer to the figure below. Write your answer in a one whole sheet of paper. 1. a circle 2. three radii 3. a diameter 4. a tangent 5. a secant 6. three chords 7. point of tangency 8. central angle 9. four minor arcs 10. at least two major arcs B. Indicate whether each statement is true or false. 1. All radii of a circle are congruent. 2. A radius is a chord of a circle. 3. A line may intersect a circle at exactly one point. 4. A circle and a line may have three points in common. 5. Every chord in a circle contains two points of the circle. 6. A chord is not a diameter. 7. A secant may contain a chord. 8. A secant may pass through the centre of a circle. 9. A tangent to a circle intersects a radius. 10. All radii have the same measure. Activity Sheet Directions: Help each person decide what to do by applying your knowledge on special products on each situation. 1. Jem Boy wants to make his 8 meters square pool into a rectangular one by increasing its length by 2 m and decreasing its width by 2 m. Jem Boy asked your expertise to help him decide on certain matters. a. What will be the new dimensions of Jem Boy’s pool? b. What will be the new area of Jem Boy’s pool? What special product will be use? c. If the sides of the square pool is unknown, how will you represent its area? d. If Jem Boy does not want the area of his pool to...

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• Geometry Study Guide- Triangles Essay

  ...Geometry Study Guide Test 11 Ration: The quotient of two quantities which are measured in the same unit. Proportion: Two equal ratios. 1. Theorem: In a proportion the product of the means equals to the product of the extemes. a:b = c:d - b and c are the means. -a and d are extremes. Theorems 2. If a line parallel to one side of a triangle cuts off of a triangle that is similar to the original. 3. If 2 triangles are similar then their corresponding sides are in proportion. 4. If a line parallel to one side of a triangle divides the other two sides proportionally. 5. If a line is drawn in a triangle and divides two sides proportionally, then it is parallel to the third side. 6. The line segment joining the midpoints of two sides of a triangle is parallel to the third and is ½ the length of the third. 7. Triangles are similar if two pairs of corresponding angles are congruent (a.a≅ 8. a.a). 9. Triangles are similar if all pairs of corresponding sides are in proportion. 10. A line parallel to one side of a triangle and intersecting the other two sides cuts off a triangle similar to the original. 11. Two right triangles are similar if an acute angle of one triangle is congruent to an acute angle of the other. 12. The lengths of corresponding (altitudes, corresponding...

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• Applicatios of geometry Research Paper

  ...Geometry was throughly organized in about 300 B.C, when the Greek mathematician, Euclid gathered what was known at the time; added original book of his ownand arranged 465 propositions into 13 books called Elements. Geometry is the mathematics of space and shape, which is the basis of all things that exist. Understanding geometry is necessary step by understanding how the things in our world exist. The applications of geometry in real life are not always evident to teenagers, but the reality is geometry infiltratesevery facet of our daily living. Geometry was recognized to be not just for mathematicians. Anyone can benefit from the basic learning of geometry, which is to follow the lines reasoning. Geometry is one of the oldest sciences and is corcerned with questions of shape, size and relative position of figures and with properties of space. Geometry is considered an important field pf study because of its applications in daily life. Geometry is mainly divided in to two which is plane geometry and solid geometry. Plane geometry is about all kinds of two dimensional shapes such as lines, circles, and triangles. While Solid geometry is about all kinds of three dimensional shapes like polygons, prisms, pyramids, sphere and cylinder. Now, let’s...

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• Essay about Triangles

  ...NOTES 5 New Theorems: Parts of Similar Triangles Unit 6 Day 3 1) If two triangles are similar, then the perimeters are proportional to the measures of the corresponding sides. The ratio of the perimeters = scale factor. 2) If two triangles are similar, the measures of the corresponding altitudes are proportional to the measure if the corresponding sides. 3) If the two triangles are similar. The the measures of the corresponding angle bisectors fo the triangles are proportional to the measure of the corresponding sides. Ratio of angle bisectors = scale factor 4) If the two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides. Ratio of medians=scale factor SUMMARY: If triangle A is similar to triangle B then the ratio of all corresponding one dimensional lengths is = to the scale factor. 5) Angle bisector proportionality theorem An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides. Classwork Parts of Similar Triangles Unit 6 Day 3 Find the value of each variable in each figure below. ...

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• Geometry in Golf Research Paper

  ...“Bringing it all Together: The Geometry of Golf” Golf in Geometry?? No Way! Geometry In The Game of Golf For hundreds of years, golf has been an extremely popular and growing sport all around the world. Looking where golf is now, it is growing rapidly from the young to the elder population. The first round of gold was first played in the 15th century off the coast of Scotland, but it did not start to be played until around 1755. The standard rules of golf were written by a group of Edinburgh golfers. Today, people of the US, Scotland, and England, have been drawn to the game because it is fun, challenging, and hardly any athletic ability at all is required for amateurs. In breaking down the game, geometry plays a major role, and can influence a players score dramatically. Geometry plays a key role and influences aspects such as the ball, course, or golf swing. First Geometry is important in the design of the golf ball. It is crucial that the golf ball is not a perfect sphere, but as close to a sphere as possible. Before man could create the perfect golf ball, the main idea was to create a close to perfect sphere without any implications that would mess up the distance and direction of the ball. If the ball is not a perfect sphere, without any davits, the ball would not get any spin on it and would go the wrong direction. Furthermore geometry is used in...

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• Essay on Copyrights

  ...right, power and authority to enter into this Agreement; (b) Assignor is the exclusive owner of all right, title and interest, including all intellectual property rights, in the Invention and the Patent; (c) The Invention and Patent are free of any liens, security interests, encumbrances or licenses; (d) The Invention and Patent do not infringe the rights of any person or entity; (e) There are no claims, pending or threatened, with respect to Assignor's rights in the Invention and Patent; (f) This Agreement is valid, binding and enforceable in accordance with its terms; and (g) Assignor is not subject to any agreement, judgment or order inconsistent with the terms of this Agreement. (h) the Assignee can register and dispose of the copyright in the Work in the Assignee's own name. 4. Attorney's Fees Should either party hereto, or any heir, personal representative, successor or assign of either party hereto, resort to litigation to enforce this Agreement, the party prevailing in such litigation shall be entitled, in addition to such other relief as may be granted, to recover its or their reasonable attorneys' fees and costs in such litigation from the party against whom enforcement was sought. 5. Entire Agreement This Agreement, contains the entire understanding and agreement between the parties hereto with respect to its subject matter and supersedes any prior or contemporaneous written or oral agreements, representations or warranties...

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• Copyright Essay

  ...The Law of copyright is an automatic right and a property right also known as intellectual property and arises whenever an individual or company creates a piece of work. In order for this piece of work to qualify for copyright the work has to be original and display an amount of labour, skill and judgement. Work that expresses the idea in a physical and obtainable form can be protected, however an idea alone cannot The law of copyright first originated in the United Kingdom from a concept of common law, this being the statute of Anne 1709 and became statutory when the law passed in 1711. Named after Anne, Queen of Great Britain, this was the first copyright statute in the Kingdom of Great Britain, and the first full-fledged copyright statute in the world. The current copyright act in place is the Copyright, Designs and Patents Act 1988. In order for a work to be copyrighted it has to be original. The Law of copyright is an automatic right and a property right also known as intellectual property and arises whenever an individual or company creates a piece of work. In order for this piece of work to qualify for copyright the work has to be original and display an amount of labour, skill and judgement. Work that expresses the idea in a physical and obtainable form can be protected, however an idea alone cannot. The law of...

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