 | 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... | |
 | Euclid, 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 - 804 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 - 942 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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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. 
