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Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Plane and Solid Geometry - Page 176
by Arthur Schultze - 1901

## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...an angle (BAD) of the other, have the sides about the equal angles reciprocally proportional : and, triangles which have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, are equal. Let the triangles be so...

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...right-angled triangles. Thus the general properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. fig. 122. Demonstration. Let the angle...

## Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...equiangular with ABC ; and therefore (by the Corollary to the last Proposition) similar. PROP. XVII. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides about the equal angles proportional, are similar. In the triangles ABC, DEF, let the...

## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - Geometry - 1845 - 382 pages
...AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. — Equal triangles which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2) triangles which have an angle...

## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...properties of triangles include, by implication, those of all figures. FROPOSITION XIX. THEOREM.Two triangles, which have an angle of the one equal to an angle of tlie other, and the sides containing those angles proportional, are similar, In the two triangles ABC,...

## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...right, since they are equal to these right angles (by Prop. 34.) CoR. 2. — If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles will be also equal ; for the angles which are opposite to these equal angles are...

## Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...must also be proportional to the sides GH, HK ,( B. IV, Def. 3). Therefore the two triangles ABC, GHK have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently these triangles are similar ; and being...

## Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 340 pages
...(147) with (148).] Of PROPOSITION III. Two triangles, having an angle of the one equal to an (159) angle of the other, are to each other as the products of the sides about the equal angles. Let the equal apgles of the triangles A, B, be made vertical, and join the...