 | John Gibson - 1881 - 64 pages
...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 on the same base and between the same parallels are equal. 4. Equal triangles... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...of C, AC to BD, AB to CD, and the area of ABC to the area of BCD. N^ Proposition 33. ' Theorem. — Parallelograms on the same base and between the same parallels are equal. Let ABDC, EFDC be two parallels A EB p grams, on the same base CD and between ' the same parallels... | |
 | Mary W I. Shilleto - 1882 - 418 pages
...students are advised not to confine themselves to one paper, but to make use of the whole set. (a) 1. Parallelograms on the same base and between the same parallels are equal. AOC is an isosceles triangle, of which A is the vertex : AB, AC are bisected in D & E respectively... | |
 | John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...kind being worth £10 each. Find how many he has of each kind. 1. Write down the three postulates. 2. Parallelograms on the same base, and between the same parallels are equal to one another. 3. If a straight line be bisected, and produced to any point, the squares of the whole... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...how to draw a straight line through a given point, parallel to a given straight line. 11. Show that parallelograms on the same base and between the same parallels are equal. Show how to construct an isosceles triangle equal to a given triangle. '10.) 12. ABC is a triangle... | |
 | Marianne Nops - 1882 - 278 pages
...given above is easier. Only one case is given by Euclid. SUMMARY OF PROPOSITION XXXV., THEOREM 25. Parallelograms on the same base and between the same parallels are equal in area. Cons. — Nil. Case I. Each \^m is double of A DEC (I. 34). .-. Hg™™ are equal. Cases... | |
 | 1882 - 486 pages
...same side, and also the two interior angles on the same side together equal to two right angles. 4. Parallelograms on the same base, 'and between the same parallels, are equal to one another. 5. In any right-angled triangle FGH, the square which is described on the side FH,... | |
 | College of preceptors - 1882 - 528 pages
...difference of two sides of a triangle and the third side. 3. Define a parallelogram ; and show that parallelograms on the same base and between the same parallels are equal in area. Enunciate a converse of this proposition. 4. Define an acute-angled triangle, an obtuse-angled... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...4. and the diameter BG divides the parallelogram AGDB into two equal parts. PROPOSITION 85. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels... | |
 | Mathematical association - 1883 - 86 pages
...difference of identically equal magnitudes are equal, although they may not be identically equal. THEOR. 1. Parallelograms on the same base and between the same parallels are equal. COR. 1. A parallelogram is equal to a rectangle, whose base and altitude are equal to those of the... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
