| 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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