 | University of Cambridge - 1884 - 624 pages
...the specimens G — M. 3. Yivâ voce. MATHEMATICAL TKIPOS. PART I. MONDAY, May 26, 1884. 9 to 12. 1. THE opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects the parallelogram, that is, divides its into two equal parts. A rhombus is circumscribed to a rectangle.... | |
 | Euclides - 1884 - 214 pages
...Proved. therefore AC is parallel to BD, I. 27. and AC is equal to BD. Proved. Therefore, the straight lines &c. QED PROPOSITION XXXIV. THEOREM. The opposite sides and angles of a parallelogram are equal, and the diagonal bisects the parallelogram, that is, divides it into two equal parts. GIVEN that ACDB... | |
 | Euclides - 1884 - 182 pages
...parallel, the straight line bisecting both will be parallel to the remaining sides of the figure. 81. PROPOSITION XXXIV. — THEOREM. The opposite sides and angles of a parallelogram are equal toone another ; and either diameter bisects it, that is, divides it intotwo equal triangles. Let ABDC... | |
 | Education - 1885 - 630 pages
...understood abbreviations for words may be used.] Answer two Questiens, including No. 3, if you can. 1. The opposite sides and angles of a parallelogram are...equal to one another, and the diameter bisects it, that is, divides it into two equal parts. Euclid, Book I., Prop. 34. 2. In any right-angled triangle,... | |
 | Oxford univ, local exams - 1885 - 358 pages
...they do not bisect one another. 5. Inscribe in a circle a triangle equiangular to a given triangle. 6. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects the parallelogram, that is, divides it into two equal parts. 7. Describe a square which shall be equal... | |
 | 1885 - 608 pages
...witli four right angles, is equal to twice as many right angles as the figure has sides. 5. Prove that the opposite sides and angles of a parallelogram are equal to one another, and that the diagonal bisects it. 6. Divide a straight line into two parts, so that the rectangle contained... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...sides will include an angle supplemental to the vertical angle of the triangle. THEOREM XXXII. 217. The opposite sides and angles of a parallelogram are equal to one another, and each diagonal bisects it. HYPOTHESIS. Let AC be a diagonal of & ABCD (using the sign £j for the word... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...sides will include an angle supplemental to the vertical angle of the triangle. THEOREM XXXII. 217. The opposite sides and angles of a parallelogram are equal to one another, and each diagonal bisects it. HYPOTHESIS. Let AC be a diagonal of a ABCD (using the sign a for the word... | |
 | E. J. Brooksmith - Mathematics - 1889 - 356 pages
...angles AEB, AFB are equal to one another. Show that the triangles AEB, AFB are equal in all respects. 2. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects the parallelogram, that is, divides it into two equal parts. AB, CD, EF are three parallel straight... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...parallelogram are sometimes called diameters. The symbol for parallelogram is ||gm. PROPOSITION 34. THEOREM. The opposite sides and angles of a parallelogram...are equal to one another, and the diameter bisects the parallelogram, ie divides it into two equal parts. Let ACDB be a ||gm of which BC is a diameter;... | |
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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax. 
