## Geometry: Seeing, Doing, UnderstandingHarold 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 - Thruston - LibraryThingA 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. Read full review

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 |