 | Euclides - 1855 - 262 pages
...the diagonal is the straight line joining the vertices of two opposite angles. PROP. XXXIV. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it, that is, divides it into UEO equal parts. Let AD be a parallelogram, of... | |
 | 1856 - 428 pages
...to the whole angle А с D ; and the angle в А с has been proved to be equal to the angle в DC; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diagonal в с bisects the parallelogram A D. Because in the two triangles ABC and D с в, the... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...point in a given straight line to make a given rectilineal angle equal to a given rectilineal angle. 4. The opposite sides and angles of a parallelogram are equal to one another and the diameter bisects them, that is, divides them into two equal parts. 6. In any right-angled triangle,... | |
 | 1858 - 380 pages
...side. Is the same proposition true of the angles of a triangle? 3. What is a parallelogram? Prove that the opposite sides and angles of a parallelogram are equal to one another, and that the diagonal bisects it. 4. If a straight line be divided into any two parts, the rectangles... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...angle ABD is equal to the whole angle ACD. But the angle BAC has been proved equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to each other. Cor. Two parallels, AB, CD, comprehended between two other parallels, AC, BD, are equal... | |
 | Euclides - 1860 - 288 pages
...28); therefore the lines joining their extremities are equal and parallel. pROposmou xxxiv. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it; that is, divides it in two equal parts. Given a parallelogram ACDB, of... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...as well as those which bisect any two interior angles of a parallelogram, contain a right angle. 78. The opposite sides and angles of a parallelogram are equal to one another, and the diameters bisect it. State and prove the converse of this proposition. Also shew that a quadrilateral... | |
 | Euclides - 1862 - 172 pages
...equal to the whole angle ACD; (ax. 2) and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter shall bisect it. For because AB is equal to CD; and BC common, the two AB, BC, are equal... | |
 | Euclides - 1862 - 140 pages
...whole angle ACD. (ax. 2.) 7. And the angle BAC has been shown to be equal to the angle BDC (dem. 4). Therefore the opposite sides and angles of a parallelogram are equal to one another. 8. Also the diagonal bisects it, for the triangles ABC, BCD, are every way equal. (I. 26.) BOOK; 1.... | |
 | Euclides - 1863 - 122 pages
...equal (Ax. 2) to the-whole angle ACD; and the angle BAC has been proved to be equal to the angle BDC. Therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diagonal Be bisects the parallelogram AD. Because in the two triangles ABC, DCB, AB is equal to... | |
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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB... 
