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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'...
The Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 269
των Euclides - 1874
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## Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1838 - 386 σελίδες
...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 oiher, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF,...

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

Euclides - 1840 - 194 σελίδες
...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 placed...

## The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 σελίδες
...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...

## Elements of Geometry

Adrien Marie Legendre - 1841 - 235 σελίδες
...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 =...

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

Nicholas Tillinghast - 1844 - 96 σελίδες
...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,...

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

Euclid, James Thomson - 1845 - 380 σελίδες
...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...

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

Euclides - 1846 - 272 σελίδες
...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 - 1847 - 308 σελίδες
...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...

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

George Clinton Whitlock - 1848 - 324 σελίδες
...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,...

## Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - 1849 - 384 σελίδες
...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...