 | Simon Newcomb - Geometry - 1881 - 418 pages
...Angle A — angle FMN = angle D; ) ,„. Angle B = angle FMN = angle E. \ ^ ' QED THEOREM VII. 393. Two triangles having one angle of the one equal to one angle of the other, and the sides containing these angles proportional, are similar. Hypothesis. ABC and A'B'C', two triangles... | |
 | Education, Higher - 1884 - 538 pages
...homologous sides shall either be equal, or be together equal to two right angles. 15. Triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Algebra. Junior, Senior,... | |
 | George Bruce Halsted - Measurement - 1881 - 266 pages
...ratio m:n, and its area E. f^jj l^g « = •»/ ; 0=-\l — . Ans. \ n \ m 521. If two triangles have one angle of the one equal to one angle of the other, and the sides about a second angle in each equal, then the third angles will be either equal or supplemental.... | |
 | Education, Higher - 1883 - 536 pages
...other, have their sides about the equal angels 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. 15. If... | |
 | John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...nearer to the centre than the less. 7. Define equal triangles, and prove that if equal triangles have one angle of the one equal to one angle of the other, then the sides about the equal angles are reciprocally proportional. GENEEAL PAPEE. 1. Trace very briefly... | |
 | Mathematical association - 1883 - 86 pages
...those sides which are opposite to the equal angles are homologous. THEOR. 3. If two triangles have one angle of the one equal to one angle of the other and the sides about these angles proportional, they are similar, and those angles which are opposite... | |
 | University of Glasgow - 1883 - 438 pages
...of the radins of the circle to the side of the second square ? 12. Prove that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles are similar. 14. One of the parallel... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...to the triangle DEF. Wherefore, if the sides &c. QED 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 equiangular to one another,... | |
 | University of Cambridge - 1884 - 624 pages
...same ratio which the other sides of the triangle have to one another. 9. 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. THURSDAY, December 6, 1883. 9— ARITHMETIC. (A) 1. MULTIPLY fifty thousand... | |
 | 1884 - 610 pages
...given circle. Inscribe a regular figure of ten sides in a given circle. 3. 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. If one of the said sides in the one triangle be equal to one of the said... | |
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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. 
