 | Popular educator - 1854 - 922 pages
...whole angle A c D ; and the angle ВАС has been proved to be equal to the angle в D с ; therefore the opposite sides and angles of a parallelogram are equal to one another. Abo the diagonal в с bisects the parallelogram A D. Because in the two triangles ABC and D с в,... | |
 | Euclides - 1855 - 270 pages
...the whole angle A СD. And the angle BAС has been proved to be equal to the angle BD С. Therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diagonal B С bisects the parallelogram AD. Because in the two triangles ABС, DСB, AB is... | |
 | 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 contained... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...Hence the sum of the exterior angles must be equal to four right angles (Axiom 3). PROPOSITION XXIX. THEOREM. The opposite sides and angles of a parallelogram are equal to each other. Let ABDC be a parallelogram ; then will AB its opposite sides and angles be equal to each... | |
 | Euclides - 1860 - 288 pages
...parallel (I. 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 which... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...to the whole angle A CD ; (ax. 2.) and the angle BA C has been shewn to be equal to BDC; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter .BCbisects it. For since AB is equal to CD, and BC common, the two sides AB, BC,... | |
 | Euclides - 1862 - 140 pages
...and it was shown to be equal to it. (dem. 4.) Conclusion. — Therefore, the straight lines, &c. QED PROPOSITION 34.— THEOREM. The opposite sides and...angles of a parallelogram are equal to one another, and the diagonal bisects it, that is, divides it into two equal parts. (References— Prop. I. 26, 29;... | |
 | Euclides - 1862 - 172 pages
...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... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...rectangle contained by the whole and one of the parts may be equal to the square on the other part. 4. 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. 5. To a given straight... | |
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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. 
