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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.
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 90
by Dennis M'Curdy - 1846 - 138 pages

## Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880 - 396 pages
...circle are equal to one another. 9. Define — .similar rectilineal figures, and reciprocal figures. 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...

## Metrical Geometry: An Elementary Treatise on Mensuration

George Bruce Halsted - Measurement - 1881 - 266 pages
...rectangle from their 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...

## Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...produced portion of such sides is equal to the rectangle of the sides of the parallelogram. THEOREM 8. If two triangles have one angle of the one equal to one angle of the other, and the perpendiculars from the other two angles upon the opposite sides proportional,...

## The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1882 - 286 pages
...Therefore ABC, DEF are also equiangular, and therefore (V. 4) similar. 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 proportional, the triangles will be similar....

## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1883 - 376 pages
...shew that the lines BC, be divide each other in reciprocal proportion. And Conversely, Trianyks, which have one angle of the one equal to one of the other, and their sides about the equal angles reciprocally proportional, are eqiud to one another. Let the sides...

## Glasgow University Calendar

University of Glasgow - 1883 - 438 pages
...square. What is the 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....

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

Mathematical association - 1883 - 86 pages
...they are 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 Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...proportional> but not their angles equal. VI. 7. In VI. 7 the enunciation is imperfect ; it should be, "if two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, to that the sides subtending...