 | Mary W I. Shilleto - 1882 - 418 pages
...two given points draw two lines, forming with a line given in position, an equilateral triangle. 3. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects the parallelogram, that is, divides it into two equal parts. If from the base... | |
 | 1882 - 480 pages
...of that which has the greater contained angle is greater than the base of the other. 8. Prove that the opposite sides and angles of a parallelogram are equal to one another ; and that the diagonal of a parallelogram bisects it. 4. On a given straight line construct a parallelogram... | |
 | Moffatt and Paige - 1883 - 514 pages
...angle ABD is equal to the whole angle ACD (Ax. 2). And the angle BAG has been proved equal to BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter BC bisects it. For since, in the triangles ABC, BCD, AB is equal to CD, and BC is common... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...And it was shewn to be equal to it. Wherefore, the straight lines &c. QEI). PROPOSITION 34. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diameter Insects the parallelogram, that is, divides it into two equal parts. Let ACDB be a... | |
 | Euclides - 1883 - 176 pages
...sides of a triangle, they shall form a triangle equiangular to the given triangle. PROP. 34. THEOR. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it. Given ABCD, a parallelogram, AB ie, given AB || DC, and AD || BC; let... | |
 | Stewart W. and co - 1884 - 272 pages
...opposite sides and angles of parallelograms are equal to one another; also, their diameter bisects them ; for AB being equal to CD, and BC common, the two AB,...DC, CB, each to each; and the angle ABC is equal to BCD ; therefore the triangle ABC is equrj to BCD. AE J> J1 XXXV. — Parallelograms upon the same base,... | |
 | Euclides - 1884 - 182 pages
...third sides equal. (8) 8. Any two angles of a triangle are together less than two right angles. (8) 9. The opposite sides and angles of a parallelogram are equal to one another. (9) 10. If two isosceles triangles have the same base, the lino which joins their summits is at right... | |
 | 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... | |
 | 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.... | |
 | 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... | |
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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB... 
