| T S. Taylor - 1880 - 152 pages
...enunciations of Euc. I. 26 and I. 29; and Axiom 2, and the definition of a parallelogram. General Enunciation. **The opposite sides and angles of a parallelogram are equal to one another.** Particular Enunciation. Given. — The parallelogram AB CD. Required. — To prove that (a) AB is equal... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...And it was shewn to be equal to it. Wherefore, the straight lines &c. QED PROPOSITION 3i. THEOREM. **The opposite sides and angles of a parallelogram are equal to one another,** and the diameter bisects tJie parallelogram, that is, divides it into two equal parts. Note. A parallelogram... | |
| Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...bisecting AB and AC in D and F respectively is parallel to the base BC. PROP. XXXIV. THEOREM. Th/>, **opposite sides and angles of a parallelogram are equal to one another,** and tlie diameter bisects the parallelogram, that is, divides it into two equal parts. Let ABDC be... | |
| John Gibson - 1881 - 64 pages
...be parallel to the base, prove that the triangle is isosceles. TEST PAPER E. Propositions 33-40. 1. **The opposite sides and angles of a parallelogram are equal to one another.** 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. Triangles... | |
| John Carroll (art master.) - Geometry - 1881 - 100 pages
...&c. :; HO LESSON XIX.— RECTILINEAL FIGURES INSCRIBED IN AND DESCRIBED ABOUT OTHERS— Continued. " **The opposite sides (and angles) of a parallelogram are equal to one another."** — Euclid i. 34. Problem 118. — Within any quadrilateral figure V WX Y to inscribe a parallelogram,... | |
| John Gibson - 1881 - 302 pages
...straight lines FH, FK are less than the two sides GH, GK but contain a greater angle. 3. Prove that **the opposite sides and angles of a parallelogram are equal to one another,** and that the diameter bisects the parallelogram. 4. Prove that parallelograms upon the same base and... | |
| Education, Higher - 1884 - 538 pages
...line drawn through the point of bisection to meet the two lines will be bisected in that point. 6. **The opposite sides and angles of a parallelogram are equal to one another** and the diagonal bisects it. If both diagonals be drawn they bisect each other. 8. If a straight line... | |
| Euclides - Euclid's Elements - 1881 - 236 pages
...equal to CD, and BC common to the two triangles ABC, DCB ; the two sides AB, BC, are equal c — 1. **to the two DC, CB, each to each. And the angle ABC** was proved to he equal to the angle BCD. Therefore the base AC is equal (I. 4) to the base BD, and... | |
| John Carroll (art master.) - Geometry - 1881 - 100 pages
...Fig.lU. wzv LESSON XIX.— RECTILINEAL FIGURES INSCRIBED IN AND DESCRIBED ABOUT OTHERS— Continued. " **The opposite sides (and angles) of a parallelogram are equal to one** ,_ another." — Euclid i. 34. Problem 118. — Within any quadii'lateral figure VWXY to inscribe a... | |
| Marianne Nops - 1882 - 278 pages
...shown 'to be equal to it. Wherefore the straight lines, &c. — QED PROPOSITION XXXIV., THEOREM 24. **The opposite sides and angles of a parallelogram are equal to one another,** and the diameter bisects it. Let ACDB be a Ig*m. of which BC is a diameter. Then shall AB = DC, and... | |
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