# Geometry: Seeing, Doing, Understanding

Macmillan, 2003 - Mathematics - 780 pages
Harold Jacobs's Geometry created a revolution in the approach to teaching this subject, one that gave rise to many ideas now seen in the NCTM Standards.  Since its publication nearly one million students have used this legendary text.  Suitable for either classroom use or self-paced study, it uses innovative discussions, cartoons, anecdotes, examples, and exercises that unfailingly capture and hold student interest.

This edition is the Jacobs for a new generation.  It has all the features that have kept the text in class by itself for nearly 3 decades, all in a thoroughly revised, full-color presentation that shows today's students how fun geometry can be.  The text remains proof-based although the presentation is in the less formal paragraph format. The approach focuses on guided discovery to help students develop geometric intuition.

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#### LibraryThing Review

User Review - LibraryThing

A stunning visual treat combined with imaginative and compelling examples from a vast range of cultures and professions that bring elementary geometry to life in a unique way.

User Review - Flag as inappropriate

I am a Geometry teacher and have taught now from three different texts (McGraw-Hill, Glencoe and Jacobs). The Jacobs text surpasses the others in so many ways. His passion for the subject is infectious, he steps through every concept logically in small steps, and he uses liberal doses of humor. It is not a typical math text designed for rote learning. You cannot flip to the lesson and see a series of examples identical to the homework, which is why some tutors don't like it. This text was designed to teach students to reason and think. At that, it excels.

### Contents

 Euclid the Surfer and the Spotter 1 Angles in Measuring the Earth 13 Telling Time with Shadows 24 We Cant Co On Like This 31 2 41 Direct Proof 50 A Deductive System 60 Lines and Angles 77
 Proportions in a Right Triangle 428 The Pythagorean Theorem Revisited 434 Isosceles and 3060 Right Triangles 441 The Tangent Ratio 448 The Sine and Cosine Ratios 454 Slope 461 The Laws of Sines and Cosines 468 Summary and Review 475

 4 131 Polygons and Congruence 139 ASA and SAS Congruence 146 Isosceles and Equilateral Triangles 157 SSS Congruence 163 Constructions 169 Summary and Review 1 76 176 Inequalities 183 The Exterior Angle Theorem 190 The Triangle Inequality Theorem 200 Parallel Lines 211 Proving Lines Parallel 219 The Parallel Postulate 225 The Angles of a Triangle 236 AAS and HL Congruence 242 7 257 Parallelograms and Point Symmetry 265 Rectangles Rhombuses and Squares 276 The Midsegment Theorem 286 Transformations 297 Reflections 305 Isometries and Congruence 312 Transformations and Symmetry 319 Midterm Review 330 Area 338 Squares and Rectangles 344 Triangles 351 Parallelograms and Trapezoids 358 The Pythagorean Theorem 365 Summary and Review 371 Algebra Review 376 Similarity 377 Ratio and Proportion 378 Similar Figures 385 The SideSplitter Theorem 392 The AA Similarity Theorem 399 Proportions and Dilations 407 Perimeters and Areas of Similar Figures 414 Summary and Review 420 Algebra Reviews 425 11 426 The Right Triangle 427
 Algebra Review 481 Circles Radii and Chords 484 Tangents 491 Central Angles and Arcs 497 Inscribed Angles 504 Secant Angles 510 Tangent Segments and Intersecting Chords 516 Summary and Review 522 Algebra Review 527 13 528 The Concurrence Theorems 529 Triangles and Circles 530 Cyclic Quadrilaterals 536 Incircles 542 The Centroid of a Triangle 548 Cevas Theorem 554 Napoleons Discovery and Other Surprises 561 Summary and Review 566 14 567 Regular Polygons and the Circle 571 Regular Polygons 572 The Perimeter of a Regular Polygon 579 The Area of a Regular Polygon 585 From Polygons to Pi 591 The Area of a Circle 598 Sectors and Arcs 605 Summary and Review 612 Geometric Solids 617 Rectangular Solids 628 Prisms 634 The Volume of a Prism 640 Pyramids 647 Cylinders and Cones 654 Spheres 662 Similar Solids 670 The Regular Polyhedra 677 16 689 The Saccheri Quadrilateral 696 The Geometries of Lobachevsky and Riemann 702 Final Review 718 Copyright