If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. A Shorter Geometry - Page xviLimited preview - About this book
| M. J. M. HILL - 1900
...PROPOSITION XLVIII. (i). (Euc. VI. 14, 1st Part.) ENUNCIATION. Parallelograms having equal areas and having **one angle of the one equal to one angle of the other** have the sides about the equal angles reciprocally proportional. Let the two parallelograms be placed... | |
| University of Toronto - 1901
...B. Similar triangles are to each other in the duplicate ratio of their homologous sides. (VI. 19.) **5. If two triangles have one angle of the one equal to one angle of the other and the sides about** one other angle in each proportional, so that the sides opposite to the equal angles are homologous,... | |
| Macmillan & Co - Textbooks - 1901 - 776 pages
...; .:, by addition, . a + b+e+ ... x+y+z+ ... or a:x 338 EUCLID'S ELEMENTS. PROPOSITION 6. THEOREM. **If two triangles have one angle of the one equal to one angle of the other, and the sides about** the equal angles proportionals, the triangles shall be similar. In the A' BAG, EOF, let the L. BAG... | |
| Eldred John Brooksmith - Mathematics - 1901
...diameters. 10. Describe a circle about a given equilateral and equiangular pentagon. 11. Triangles which **have one angle of the one equal to one angle of the other and the sides about** the equal angles reciprocally proportional, are equal to one another. , Two straight lines AOC, BOD... | |
| Thomas Franklin Holgate - Geometry - 1901 - 440 pages
...vertex of the right angle which make equal angles with one of the sides. MISCELLANEOUS EXERCISES 1. **If two triangles have one angle of the one equal to one angle of the other, and** a second angle of the one supplementary to a second angle of the other, then the sides about the third... | |
| 1902
...of the sides and conversely. Prove that the bisectors of the angles of a triangle are concurrent. 4. **If two triangles have one angle of the one equal to...of the other and the sides about these equal angles** proportionals the triangles will he similar. In two different circles chords which subtend equal angles... | |
| Education - 1902
...pentagon is equal to the sum of a side and a diagonal of the smaller pentagon. 5. Equal triangles, which **have one angle of the one equal to one angle of the other,** have their sides about the equal angles reciprocally proportional. 12, ABCD is a trapezium in which... | |
| Olaus Henrici, George Charles Turner - Electronic book - 1903 - 204 pages
...negative. Geometrically the theorem is that of Euc. VI. vi., from which the general case follows at once. " **If two triangles have one angle of the one equal to one angle of the other and the sides about** the equal angles proportionals, the triangles shall be similar." For if one triangle be applied to... | |
| 1903
...that the square on DE is equal to twice the rectangle contained by the radii of the two circles. 4. **If two triangles have one angle of the one equal to one** an^le of the other, and the sides about the equal angles proportionals, show that the triangles are... | |
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