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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. Plane Geometry - Page 180by Arthur Schultze - 1901Full view - About this book
| Timothy Walker - Geometry - 1829 - 156 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... | |
| 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... | |
| Mathematics - 1835 - 684 pages
...interjacent side (c). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . cor. 14 5. **An angle of the one equal to an angle of the other,** and the sides about two other angles, each to each, and the remaining angles of the same affection,... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...general properties of triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. **Two triangles, which have an angle of the one equal to an angle of the other,** and the sides containing those angles proportional are similar, In the two triangles ABC, DEF, let... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...8.) is the difference between DER and the sum of the other two triangles. 86. Lemma. If two triangles **have an angle of the one equal to an angle of the other** ; and the sides which include the angle in one triangle are supple- 1887) ments of those which include... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...is the difference between DER and the surn of the other two triangles. 86. Lemma. If two triangles **have an angle of the one equal to an angle of the other** ; and the sides which include the angle in one triangle are supplements of those which include it in... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...parallelogram AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. EQUAL **triangles which have an angle of the one equal to an angle of the other,** have their sides about those angles reciprocally proportional : and (2.) triangles which have an angle... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...equilateral or equiangular with respect to each other, are equivalent. 467. Lemma. If two triangles **have an angle of the one equal to an angle of the other** ; and the sides which include the angle in one triangle are supplements of those which include it in... | |
| Adrien Marie Legendre - Geometry - 1838 - 382 pages
...general properties of triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. **Two triangles, which have an angle of the one equal to an angle of the** oiher, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF,... | |
| Euclides - 1840 - 192 pages
...an angle (BAD) of the other, have the sides about the equal angles reciprocally proportional : and, **triangles which have an angle of the one equal to an angle of the other,** and the sides about the equal angles reciprocally proportional, are equal. Let the triangles be so... | |
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