The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... Elements of Plane Geometry: For the Use of Schools - Page 71by Nicholas Tillinghast - 1844 - 96 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...triangles. Thus the general properties of triangles involve those of all figures. j THEOREM. / (I 208. **Two triangles, which have an angle of the one equal to an angle of the other and the sides about** these angles proportional, are similar. Demonstration. Let the angle A = D (fig. 122), and let Fig.... | |
| Adrien Marie Legendre - 1825 - 570 pages
...properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an ungle **of the one equal to an angle of the other and the sides about** these angles proportional, are similar. Demonstration. Let the angle A = D (fig. 122), and let Kig.... | |
| Euclides - 1826 - 226 pages
...their sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one **angle of the other, and the sides about the equal angles proportional,** the triangles shall be equiangular, and have those angles equal which subtend the homologous sides,... | |
| Euclid - 1826 - 236 pages
...their «ides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one **angle of the other, and the sides about the equal angles proportional,** the triangles shall be equiangular, and have those angles equal which subtend the homologous sides.... | |
| George Darley - Geometry - 1828 - 190 pages
...proportional, are equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, **which have an angle of the one equal to an angle of the other.** For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road... | |
| Walter Henry Burton - Astronomy - 1828 - 84 pages
...F, are equal; and so, if 'the angles at F had been supposed equal, the triangles would have had each **angle of the one equal to an angle of the other, and the** side CF lying between correspondent angles in each; whence also DF is equal to FE. Is this sufficiently... | |
| Timothy Walker - Geometry - 1829 - 158 pages
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they **have an angle of the one equal to an angle of the other, and the sides** including these angles proportional. Thus if the angle A = A (fig. 45), and if AB : AD : : AC : AF,... | |
| James Hayward - Geometry - 1829 - 218 pages
...suppress , BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles **have an angle of the one equal to an angle of the other,** their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take... | |
| John Playfair - Geometry - 1829 - 186 pages
...proportional, the triangles will be equiangular. If two triangles have,one angle of one triangle equal to one **angle of the other, and the sides about the equal angles proportional,** the triangles will be equiangular. Equal parallelograms, and also equal triangles, which have one angle... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...side (r). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . »r. 14 5. Au **angle of the one equal to an angle of the other, and the sides about** two other angles, each to each, and the remaining an;;!« of the same affection, or one of them a right... | |
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