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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. "
The First Six Books: Together with the Eleventh and Twelfth - Page 170
by Euclid - 1781 - 520 pages
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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 pages
...the line joining two alternate vertices of a given length. 7. Prove that equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 8. In a right-angled triangle, show...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...parallelograms as in VI. 23, ||gm AC : ||gm CF :: rect. BC, CD : rect. EC, CG. Ex. 717. — Triangles which have one angle of the one equal to one angle of the other are to one another in the ratio compounded of the ratios of the sides containing the equal angles....
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
....-. a AC = a BF. (/3) is true. EUCLID Proposition 15. THEOREMS — (a) Triangles of equal area which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : (/3) and conversely, if two triangles...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1890
...segments of the base. What is the corresponding proposition for the external bisector ? 8. 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 the sides about the equal angles....
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Annual Report of the Chief Superintendent of Education

1891
...and those which are opposite to the equal angles are homologous sides. 6. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. NB — Female candidates will receive...
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Annual Report of the Department of Education

New Brunswick. Board of Education, New Brunswick. Department of Education - Education - 1893
...IM GEOMETRY. Time, 1 hr. 30 win. 1 or 2 and all tlie rest make a full paper. 1. (a) 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 if the third angle in each be both acute, both obtuse,...
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Annual Report of the Department of Education

New Brunswick. Board of Education, New Brunswick. Department of Education - Education - 1893
...IM GEOMETRY. Time, 1 hr. 30 min. 1 or 2 and all the rest make a full paper. 1. (a) 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 if the third -angle in each be both acute, both...
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Journal of Education

Education - 1893
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1894
...than eight question*. The values attached to the questions are shown in brackets. 1. If two triangles have one angle of the one equal to one angle of the other, and the sides about these equal angles proportional, show that the triangles are similar, and that those...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...parallel or perpendicular to the sides of the other, they are similar. (Why ?) Theorem 9. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional. the triangles are similar. Given A A1 B1d, A2B2C2, such that Z d...
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