### Contents

 CHAPTER 1 Motion 8 Perpendicular lines 14 Parallel lines 23 Common tangents 33 Adjacent angles vertical angles 42 CHAPTER III 62 The isosceles triangle 69
 Loci of points 122 Construction problems 130 Construction problems 151 Properties of a proportion 157 Construction problems 163 Trigonometric ratios 174 Construction problems 182 METRIC RELATIONS 192

 Inequalities 77 Polygous in general 99 CHAPTER V 110 Regular polygons 116
 Oblique triangles 202 Regular polygons and circles 208 Measurement of arcs of a circle 214 Copyright

### Popular passages

Page 207 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 98 - The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to one-half the length of the third side.
Page 67 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 188 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 84 - ... the angle opposite the third side of the first triangle is greater than the angle opposite the third side of the second.
Page 183 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 172 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 187 - 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.
Page 160 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 150 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.