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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.
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Σελίδα 161
των Euclid - 1810 - 518 σελίδες
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## Calendar, for the Year ...

1895 - 142 σελίδες
...Being given a side of a regular pentagon, construct it. 4. Triangles which are equal in area, and which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. Describe an isosceles triangle equal...

## Calendar, for the Year ...

1897 - 154 σελίδες
...cn the same arc. Deduce that all angles in the same segment of a circle are equal to one another. 4. If two triangles have one angle of the one equal to one angle of tt;e oiher, and the sides about the equal angles proportionals, shew that the triangles are similar....

## New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1899 - 400 σελίδες
...parallel or perpendicular to the sides of the other, they are similar. PROPOSITION XVIII. 264. Theorem. 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. A, Bi Given A AiBiCi, A^B2C^, such that Z...

## New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - 1899 - 265 σελίδες
...the sides of the other, they are similar. PLANE GEOMETRY. [BK. IV. PROPOSITION XVIII. 264. Theorem. 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 AA^Ci, A2B2C2, such that Z Cl = Z (72...

## Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1899 - 348 σελίδες
...AB in D and AC in E, so that DP may be a fourth part of PE. Dl 44. Prove that equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional ; and state and prove the converse...

## Proceedings of the Edinburgh Mathematical Society

Edinburgh Mathematical Society - 1899 - 342 σελίδες
...joined, the triangles EAB, DAC are halves of the parallelograms BE, CD. Hence, Two triangles which have one angle of the one equal to one angle of the other have to each other the same ratio as the rectangles contained by the sides about the equal angles....

## Examination Papers

University of Toronto - 1900 - 1160 σελίδες
...the other, have their sides about the equal angles reciprocally proportional ; and 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. Use this proportion...

## The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 190 σελίδες
...about the equal angles reciprocally proportional, are equal in area. 49. (i) 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. (ii) Triangles which have one angle...

## The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 165 σελίδες
...PROPOSITION XLVIII. (i). (Euc. VI. 14, 1st Part.) ENUNCIATION. Parallelograms having equal areas and having one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional. Let the two parallelograms be placed...

## Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 462 σελίδες
...vertex of the right angle which make equal angles with one of the sides. MISCELLANEOUS EXERCISES 1. 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...