# Plane and Solid Geometry

Scott, Foresman, 1918 - Geometry - 436 pages

### Contents

 Preliminary Statement 7 Symbols and Abbreviations 16 Fundamental Principles 29 Triangles 38 Axioms of Equality 45 Quadrilaterals 61 Inequalities 69 Concurrent Lines 80
 Trigonometric Ratios 219 REGULAR POLYGONS MEASUREMENT OF CIRCLES 231 Measurement of the Circle 243 Computation of π 251 Maxima and Minima 264 Symmetry 270 STRAIGHT LINES AND PLANES 277 Lines and Planes Parallel 283

 Methods of Proof 89 General Exercises 96 THE CIRCLE 103 Tangents and Secants 110 Angle Measurement 116 Problems of Construction 125 Location of Points Loci 133 AREAS OF POLYGONS 145 The Parallelogram 155 Practical Methods 162 Theorem of Pythagoras 16 165 Transformations and Constructions 174 General Exercises 180 PROPORTION AND SIMILARITY 187 Similarity 200 Similar Polygons 210
 Projections 293 Polyedral Angles 302 Loci 307 POLYEDRONS PRISMS CYLINDERS 313 fongruent and Equivalent Solids 324 General Exercises 339 Areas of Pyramids and Cones 349 Volumes of Pyramids and Cones 357 Similar Pyramids and Cones 365 Polyedrons 373 General Exercises 379 Distance on a Sphere 386 Relative Positions of Spheres 392 Polar Triangles 415 General Exercises 424 Copyright

### Popular passages

Page 169 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Page 75 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 19 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Page 155 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 89 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 164 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.
Page 155 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 248 - ... as the squares of their radii, or as the squares of their...
Page 296 - Axiom. Through a given point only one straight line can be drawn parallel to a given straight line.
Page 39 - In an isosceles triangle the angles opposite the equal sides are equal.