| Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 190 pages
...about the equal angles reciprocally proportional, are equal in area. 49. (i) 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. (ii) Triangles which have one angle... | |
| Euclides, Micaiah John Muller Hill - Euclid's Elements - 1900 - 165 pages
...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... | |
| Macmillan & Co - Textbooks - 1901 - 802 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 - 368 pages
...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 - 462 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... | |
| Education - 1902 - 940 pages
...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... | |
| Education - 1903 - 692 pages
...converse. If two triangles are equiangular their corresponding sides are proportional ; and the converse. **If two triangles have one angle of the one equal to one angle of the other and the sides about** these equal angles proportional, the triangles are similar. The internal bisector of an angle of a... | |
| Olaus Henrici, George Charles Turner - Graphic statics - 1903 - 236 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... | |
| Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...§AB, OQ = J5 AC ; join PQ ; measure L.' P, Q, and compare them with L.' B, C. =o fig. 313. THEOREM 5. **If two triangles have one angle of the one equal to one angle of the other and the sides about** these equal angles proportional, the triangles are similar. fig. 314. Data ABC, DEF are two triangles... | |
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