PARVARL COPYRIGHT, 1899, BY GEORGE WENTWORTH COPYRIGHT, 1911, 1912, BY GEORGE WENTWORTH AND DAVID EUGENE SMITH ALL RIGHTS RESERVED 819.9 The Athenæum Press GINN AND COMPANY. PROPRIETORS BOSTON U.S.A. PREFACE This book is intended for teachers, and for teachers only. The publishers will sell it to no persons except teachers of the Wentworth-Smith Geometry. Every teacher must consider himself in honor bound not to leave his copy where pupils can have access to it, and not to sell his copy except to the publishers, Messrs. Ginn and Company. It is hoped that young teachers will derive great help from studying the systematic solutions of the exercises, and that every teacher who is pressed for time will find great relief by not being obliged to work out every problem himself. Criticisms and corrections will be thankfully received. GEORGE WENTWORTH PLANE GEOMETRY TEACHERS' EDITION INTRODUCTION Exercise 1. Page 8 1. From a given point on a given straight line required to draw a perpendicular to the line. Let AB be the given line and P be the given point. It is required to draw from P a line perpendicular to AB. With P as a center and any convenient radius draw arcs cutting AB at X and Y. P ने B With X as a center and XY as a radius draw a circle, and with Y as a center and the same radius draw another circle, and call one intersection of the circles C. With a straightedge draw a line from P to C, and this will be the perpendicular required. 2. From a given point outside a given straight line required to let fall a perpendicular to the line. Let AB be the given straight line and P be the given point. It is required to draw from P a line perpendicular to AB. P A X With P as a center and any convenient radius draw an arc cutting AB at X and Y. With X as a center and any convenient radius draw a circle, and with Y as a center and the same radius draw another circle, and call one intersection of the circles C. With a straightedge draw a straight line from P to C, and this will be the perpendicular required. |