A Key To Elementary Geometry

A KEY TO ELEMENTARY GEOMETRY I5Y W. M. BAKER, MA AND A. A. BOURNE, M. A. LONDON G. BELL AND SONS, LTD. 1917 First published 1904. Second Edition revised, 1906. Third Edition revised, 1900. Fourth Edition revised, 1913. Fifth Edition revised, 1917. GLASGOW. PRINTED AT THB UNIVERSITY PRESS BY ROBERT MACLK OSE AN1 JO. LTD. CONTENTS ADDITIONAL EXERCISES xvn. 29-39, xxv. 39-81, LXV. 4-8, 173-174 174-177 178 KEY TO ELEMENTARY GEOMETRY. EXERCISES A, 14. Place a straight ruler with its edge against the two end points of the line. Trace a straight line between these points by means of the ruler. If the two lines coincide, the original line is straight. 15. Take any two points A and B on a piece of paper, and place the edge of the ruler against them. Trace a line from A to B along the edge of the ruler. Again place the edge of the ruler against the points A and B, the ruler being on the other side of the line AB. Again trace a line from A to B as before. If these two lines coincide, the ruler is straight. 16. Place the straight edge of a ruler on the surface. If in all positions of the ruler the surface touches the edge oi the ruler at every point, the surface is flat. 18. Two planes intersect in a straight line. EXERCISES B, 1. 3 in. 7 62 cms. .. 1 in. 25 4 mm. 2. 4 in. 10 16 cms. nearly . 1 in. 25-4 mm. 3. 6 cms. 2-36 in. .-. 1 cm. 39 in. 4 in. to the nearest tenth. 4. 8 cms. 3 15 in. .-. 1 cm. 39 in. 4 in. ... 5. 11 45 cms. 4 in. nearly. A 2 KEY TO ELEMENTARY GEOMETRY. IBookt EXERCISES 0. 6, Cut them out and superimpose them. 8. 360, 120, 180, 240. 9. 30, 7, 22. 10. 90, 150, 240, 15, 75, 187. 14. The angles are rt. LS. 17. If the perpendicular is drawn along the edge AB of the set-sq. ABC, turn the set-square over, so that C lies on the other side of AB. Trace another line along the edge AB. If the two lines coincide the perpendicular is a true one. 23. Any two sides together the third. 30. In an isosceles A. 31. They meet in a pt. This pt. is a pt. of trisection of each. EXERCISES D. 2. 90. 3. 90. 4. 90. 5. 90. EXERCISES E. 2. A regular hexagon. 3. A square. EXERCISES G. 3. See Book I, Prop. 31, first method. EXERCISES H. 3. Make a crease ABC. Fold again so that BC falls along BA. If DBE is the second crease, DBC is a rt. L. A fola along DC makes DBC a rt. Ld. A. 4. Make a crease ABC, and, as in Example 3 above, a second crease DBE at rt. . s to it. Fold the double thick ness again along DC, and we have an isos. A. 5. Fold so that BC falls along CA, and the crease is at rt. . s to ABC at C. 6. Fold the paper about AB. Mark or prick through the pt. D where C falls. CD when joined is the reqd. line. Ex. C-P1 KEY TO ELEMENTARY GEOMETRY. 3 9. Make two creases at rt. L to any st. line AB as in Example 5. These two creases are parallel. 10. and 11. Use the methods of Examples 5 and 9. EXERCISES E. 11. By compasses set off an equal length on one of the lines of the paper. 12. 3-6 miles. 13. 3-6 miles. 14. 1914 yards. 15. 8ft. 16. Let ABCD be the larger sq., CEFG the smaller, G lying in CD, and BCE being a str. line. In CB take a pt. H such that CH GD. Join FH and cut along the line FH. Also join AH and cut along the line AH. AFEH fitted into . FGD, so that FE coincides with FG, and EH falls along GD, and AAHB placed so that AB coincides with AD, and BH is in a str. line with GD, will form a square. 19. On squared paper take AB 4 half inches long, to repre sent the support in.represents 1 foot. Along the line thro. B take BC 3 half inches long. AC 2 3 2 4 2 Exercises D. 2, and AC 5 half in. Produce CA to D, making AD AC. Read off the perp. distance of D from CB produced. This is equal to 8 half inches . the end of the see-saw can rise 8 ft. from the ground. Also by measurement the L reqd. L ACB 53 21. On squared paper take AC 24 units long, and AB at rt. LB to it 10 units long. BC represents the rope. With centre B and rad. BC describe a circle meeting BA produced at D. Bead off BD and we find it to be 26 units ...