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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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 156
av Robert Simson - 1781 - 466 sider
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## The Elements of Geometry

George Bruce Halsted - 1886 - 366 sider
...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 : : FG : GH....
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## The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

...GH. Therefore AB : CD : : EF : GH. IV. 14, Part ii. QED THEOR. 14. If two triangles or parallelograms have one angle of the one equal to one angle of the other, their areas have to one another the ratio compounded of the ratios of the including sides of the first...
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## Examinations Papers

1889
...are similar, and those sides which are opposite to the equal angles are homologous. 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...
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## Annual Report of the Schools of New Brunswick

...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
...are the middle points ofAB, CD, prove that PQ_ is parallel to AC and BD. 10. 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 ; and, conversely, triangles which...
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## Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 sider
....-. 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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## Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - 1890 - 132 sider
...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 sider
...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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## Report of the Secretary for Public Instruction ...

...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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