| Elizabethan club - 1880 - 156 pages
...the other sides, and AD, £Cbe joined and intersect in E, show that the triangle AEB is isosceles. 2. **Parallelograms on the same base, and between the same parallels are equal** to each other. 3. If the sum of the squares described on two sides of a triangle is equal to the square... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...be greater than the third. How would the process fail if the last condition were not fulfilled ? 2. **Parallelograms on the same base and between the same parallels are equal** to each other. Show that if two triangles have two sides of the one equal to two sides of the other... | |
| Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...the order of the factors, hence TV(a + /3)(a-/3)=2TVj8a, which is the proposition (Art. 41, 7). 13. **Parallelograms on the same base and between the same parallels are equal.** We have (Fig. 45) BE = BA + AE = BA + xBC. Operating with V . BC x V(BC . BE)=V(BC . BA), since VaBC2... | |
| Education, Higher - 1883 - 536 pages
...and in it take any point P. Join P, A and P, B. The angle APB shall be greater than the angle ACB. 5. **Parallelograms on the same base and between the same parallels are equal** to one another. 6. Divide a given straight line into two parts, such that the difference of the squares... | |
| 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... | |
| College of preceptors - 1882 - 528 pages
...result for the 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... | |
| Marianne Nops - 1882 - 278 pages
...parallelograms are equal. It is plain that we want a connecting link in order to compare them. We know **that parallelograms on the same base and between the same parallels are equal** ; can •we construct a parallelogram on BC and between these parallels, which will then be equal to... | |
| 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... | |
| 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,... | |
| 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... | |
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