| 1894
...described ? In what proposition does Euclid imply the fact that there can be more than one ? 2. Prove **that triangles on the same base and between the same parallels are equal** to each other. Through a given point in the base of a triangle draw a straight line bisecting the triangle.... | |
| 1894
...triangle which has the greater contained angle shall be greater than the base of the other. I. 24. 8. **Triangles on the same base and between the same parallels are equal** in area. I. 37. 9 To describe a parallelogram equal to any given rectilineal figure, and having an... | |
| Thomas Aloysius O'Donahue - 1896 - 163 páginas
...method of casting out areas is that known as " equalising," which is based on Euclid's proposition of " **triangles on the same base and between the same parallels are equal."** The method consists in constructing a triangle equal to the figure, the area of which is required,... | |
| Great Britain. Education Department. Department of Science and Art - 1899
...rectilineal figure equals seven-eighths of two right angles, find the number of sides. (12.) 10. Show **that triangles on the same base and between the same parallels are equal** in area. ABCD is a parallelogram, and P is a point within the angle formed by DC and the prolongation... | |
| Seymour Eaton - 1899 - 340 páginas
...EBCH. Therefore the parallelogram ABCD is equal to the parallelogram EFQII. PROPOSITION 37. THEOREM **Triangles on the same base, and between the same parallels, are equal.** Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD, BC ; then the... | |
| Manitoba. Department of Education - 1900
...drawn from two angles of a triangle and terminated by the opposite sides can bisect one another. 4. Two **.triangles on the same base and between the same parallels are equal.** By means of this proposition show how to describe a triangle equal to a given quadrilateral ; and Bisect... | |
| Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 páginas
...(ii) Parallelograms on equal bases and of equal altitudes are equal in area. PROPOSITION 37. THEOREM. **Triangles on the same base, and between the same parallels, are equal** in area. Let the triangles ABC, DEC be upon the same base BC, and between the same parallels BC, AD.... | |
| Euclid - 1904 - 456 páginas
...parallelogram is equal in area to a rectangle of equal base and equal altitude. PROPOSITION 37. THEOREM. **Triangles on the same base, and between the same parallels, are equal** in area. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels BC, AD.... | |
| J. W. Riley - 1905 - 500 páginas
...work it graphically, finding a rectangle of equal area. This is done by an application of the fact **that triangles on the same base and between the same parallels are equal** in area (Fig. 157, p. 93). Produce AB and join AD. Through E draw EF parallel to DA ; then the triangles... | |
| J. W. Riley - 1905 - 500 páginas
...height area = base xr — c S— . 2i The shape of the triangle does not affect the result, as all **triangles on the same base and between the same parallels are equal** in area. The area of a triangle can also be determined by the following formula : \^s(s - a)(s - b)(x... | |
| |