# Plane Geometry

Scott, Foresman, 1915 - Geometry, Plane - 277 pages
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### Contents

 Preliminary Statement 7 Symbols and Abbreviations 16 Fundamental Principles 29 Triangles 38 Axioms of Equality 45 Quadrilaterals 61 Inequalities 69 Concurrent Lines 80
 AREAS OF POLYGONS 145 The Parallelogram 155 Practical Methods 162 Projection 169 Transformations and Constructions 174 General Exercises 180 PROPORTION AND SIMILARITY 187 Proportional Lines 192

 Definitions 84 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
 Similarity 200 Similar Polygons 210 Trigonometric Ratios 219 REGULAR POLYGONS MEASUREMENT OF CIRCLES 231 Measurement of the Circle 243 Computation of a 250 Maxima and Minima 264 Symmetry 270

### Popular passages

Page 179 - 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 43 - If a straight line is perpendicular to one of two parallel lines, it is perpendicular to the other also.
Page 17 - 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 145 - 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 141 - The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares on the other two sides.
Page 79 - 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 131 - ... 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 89 - Theorem. In the same circle or in equal circles, equal chords are equidistant from the center; and of two unequal chords the greater is nearer the center. Given two equal � M, M ' , with chords AB = A'B', AE > A'B', and OC, OD, O'C' �'s from center 0 to AB, AE, and from center O
Page 83 - ... the third side of the first is greater than the third side of the second.
Page 188 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.