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The areas of two triangles which have 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'...
First Part of an Elementary Treatise on Spherical Trigonometry - Page 69
by Benjamin Peirce - 1836 - 71 pages
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## The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...a mean proportional between two given straight lines. PROP. XIV. THEOR. Equal parallelograms which have an angle of the one equal to an angle of the other, have the sides about the equal angles reciprocally proportional : and parallelograms which have an...
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## An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1841 - 186 pages
...equilateral or equiangular with respect to each other, are equivalent. /'468. Lemma. If two spherical triangles have an angle of the one equal to an angle...sides which include the angle in one triangle are supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles...
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## Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...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 A = D (fig. 122),...
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## Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...equal. But the triangle AGH is similar to ABC ; therefore DEF is also similar to ABC. Hence, If any two triangles have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, those two triangles are similar. PROPOSITION XXI. THEOREM. Two...
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## Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...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 angles, C, F,be...
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## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...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...
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## 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...
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## 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 similar,...
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## Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 338 pages
...Trapezoid— -consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having an angle of the one equal to an angle of the other — consequence • 93 4. Exercises.... 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE,...
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## Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF, let the angles A...
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