Advanced Euclidean Geometry - download pdf or read online

By Alfred S. Posamentier

ISBN-10: 1930190859

ISBN-13: 9781930190856

Advanced Euclidean Geometry provides a radical assessment of the necessities of high college geometry  after which expands these techniques to complicated Euclidean geometry, to offer academics extra self belief in guiding scholar explorations and questions.

The textual content includes hundreds of thousands of illustrations created within the Geometer's Sketchpad Dynamic Geometry® software program. it truly is packaged with a CD-ROM containing over a hundred interactive sketches utilizing Sketchpad™ (assumes that the consumer has entry to the program).

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Sample text

Acquiring a truly good facility with the concept would require that more theorems be explored than time permits in the first geometry course. Familiar concurrencies such as the medians, angle bisectors, and altitudes of a triangle are mentioned but not often established by proof. Introducing a few new theorems makes the topic of concurrency quite simple and presents a new vista in Euclidean geometry. This chapter begins by demonstrating the importance of establishing concurrency. With the help of an important theorem, first published by Giovanni Ceva in 1678, we present a vari­ ety of interesting relationships and theorems.

Discover the fallacy in the following “proof”: If two opposite sides of a quadri­ lateral are congruent, then the remaining two sides must be parallel. “P r o o f ” In quadrilateral ABCD, AD = BC. Construct perpendicular bisectors OP and OQ of sides DC and AB at points P and Q, respectively. Point N is on PO . ) Because O is a point on the perpendicular bisector of DC, DO = CO. Similarly, OA = OB. We began with AD = BC. Therefore AADO = ABCO (SSS) and mAAOD = mABOC. We can easily establish that mADOP = mACOP.

By subtraction, mADBG = К mAEBG. But mADBG = 45°, FIGURE 1-33 while mACBG = 60°; thus 45° = 60°. • Parallelograms ABGF and ACDE are constructed on sides AB and AC of AABC (see Figure 1-34). ) DE and GE intersect at point P. ^ in g BC as a side, construct parallelogram BCJK so that BiC 11PA and BK = PA. From this configuration. d . 300) proposed an extension of the Pythagorean theorem. He proved that the sum of the area of parallelogram ABGF and the area of parallelogram ACDE is equal to the area of parallelogram BCJK.

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Advanced Euclidean Geometry by Alfred S. Posamentier

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