| University of Toronto - 1900
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which **have one angle of the one equal to one angle of the other and** their sides about the equal angles reciprocally proportional are equal to one another. Use this proportion... | |
| Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 143 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... | |
| 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... | |
| 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...equal angles proportionals, the triangles shall be** similar. In the A' BAG, EOF, let the L. BAG = the /_ EOF, and let BA : AC :: ED : DF. Then shall the... | |
| 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 intersect in 0 and... | |
| 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... | |
| Education - 1901
...A(f he bisected in fí, find the locus of R. 6. If two triangles have an angle of the one equal to an **angle .of the other, and the sides about the equal angles proportionals, the triangles shall** he similar. 13_ In the side ЛГ> of the triangle AUC a point I> is taken, and DE is drawn parallel... | |
| 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...equal angles proportionals, the triangles shall be** similar." For if one triangle be applied to the other so that the proportional sides are in the same... | |
| Education - 1903
...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... | |
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