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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. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ... - Pagina 236
door John Keill - 1782 - 399 pagina’s
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The Elements of Geometry

George Bruce Halsted - 1886 - 366 pagina’s
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. B = $. G, and AB : BC :...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - 1888
...intercepted between the sides of each triangle are equal to one another. THKOR. 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...
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Annual Report of the Schools of New Brunswick

New Brunswick. Board of Education - 1889
...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. N. В.- --Female candidates will...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...parallelogram ACBD ; bisect AC, BD, in E and F. Join DE, FC, cutting AB in G and H. n. 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. If ABC...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 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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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 pagina’s
...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 pagina’s
...is a mean propi. between BC and CD, L BAC is double of L B. PROPOSITION 7. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, then if each of the remaining angles be acute,...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 pagina’s
....-. 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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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. Department of 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,...
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