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Geometry and Measurement
Solutions of the Theorems, Problems and Questions,
in “ Wormell's Modern Geometry.”
EDUCATIONAL WORKS PUBLISHED BY THOMAS MURBY.
BY RICHARD WORMELL, M.A., B.Sc.
1.-Wormell's Modern Geometry: A New Course
of Plane Geometry, in which the Theory of the Science and its Practical Applications are treated simultaneously. Crown 8vo, 256 pp.
*** The explanations and illustrations of the leading problems of Geometry here treated, and the logical demonstrations of their principles, place this work amongst the very best of the kind, and its easy and graduated method makes it at once the best that has hitherto appeared. — Evening Standard.
II.-An Elementary Course of Plane Geometry.
Third Edition. Revised and Enlarged. Price 3s.
III.-An Elementary Course of Solid Geometry.
Second Edition. Price 2s. 6d. *** These works (II. & III.) are adopted by the New Brunswick Council on Education as Text-books for use in schools throughout that province. IV.- Solutions to Exercises in Solid Geometry.
Price 2s. 60.
V.-Solutions to Exercises in the Author's
Modern Geometry. Price 25. 6d. These Solutions are also adapted to the Elementary Course of Plane Geometry, (II. above,) the Exercises being the same both in that work and in the Modern Geometry.
VI.-Arithmetic for Schools and Colleges.
Revised Edition. Price 25., with answers, 35.
VII.-Graduated Arithmetic. A Selection from the
preceding work. Price 9d. VIII. Answers to Arithmetic for Schools and
Colleges. Price is.
THOMAS MURBY, 32, Bouverie Street, Fleet Street, London, E.C.
THEOREMS AND PROBLEMS.
CHAPTERS 1. AND II.
LINES AND ANGLES.
THEOREMS ON ANGLES.
1. The bisectors of the two adjacent angles formed when one straight line meets another are perpendicular to one another.
Let ACD and B C D be the adjacent angles and let C E bisect the angle A C D and CF bisect the angle BCD; then shall the angle ECF be a right angle.
Because L ECD is half ACD,
and LFCD is half BCD; :. The sum of LEC D and LFC D is half the sum of 2 ACD and <BCD;
But we know the sum of ACD and B C D to be two right angles.
:: LECF, which is the sum of ZECD and FCD, is one right angle.