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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: Also the Book of Euclid's Data ...cor. viz. The ... - Σελίδα 163
των Robert Simson - 1804
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Glasgow University Calendar

University of Glasgow - 1883
...ratio 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...

Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...similar, and those angles which are opposite to the homologous sides are equal. THEOR. 5. If two triangles have one angle of the one equal to one angle of the other, and the sides about one other angle in each proportional, so that the sides opposite the equal angles...

Examinations Papers

1884
...equiangular pentagon in a 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...

Cambridge University Examination Papers

University of Cambridge - 1884
...of the base shall have the 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....

The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...angle of the other have their sides about the equal angles reciprocally proportional. Conversely : 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. (1) Let BAC, DAE be equal...

Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

...construct a parallelogram ACBD; bisect AC, BD, in E and F. Join DE, FC, cutting AB in G and H. 11. 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. II. ARITHMETIC....

Calendar of Dalhousie College and University

Dalhousie University - 1884
...the angles of two triangles are proportional, the triangles -are equiangular. 8. Equal triangles that have one angle of the one -equal to one angle of the other, have the sides about the equal angles reciprocally proportional. Extend the enunciation, shewing why you...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

...to the circles from' any point \n Afí produced aro equal to one another. 9. Equal parallelograms, which have one angle of the one equal to one angle of the other, havo their eidos about the equal angles reciprocally proportional. FRIDAY, October 10, 1884. О—1Ц....

THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...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 :...

The Elements of Geometry

George Bruce Halsted - 1886 - 366 σελίδες
...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 :...