Books Books 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... Elements of Plane Geometry: For the Use of Schools - Page 71
by Nicholas Tillinghast - 1844 - 96 pages ## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...interjacent side (c). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . cor. 14 5. An angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining angles of the same affection, or one of them a right... ## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...the general properties of 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 and... ## First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...is the difference between DER and the surn of the other two triangles. 86. Lemma. If two triangles have an angle of the one equal to an angle of the other ; and the sides which include the angle in one triangle are supplements of those which include it in the other triangle... ## First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...8.) is the difference between DER and the sum of the other two triangles. 86. Lemma. If two triangles have an angle of the one equal to an angle of the other ; and the sides which include the angle in one triangle are supple- 1887) ments of those which include it in the other... ## An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...equilateral or equiangular with respect to each other, are equivalent. 467. Lemma. If two triangles have an angle of the one equal to an angle of the other ; and the sides which include the angle in one triangle are supplements of those which include it in the other triangle... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...parallelogram 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 Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 pages
...the general properties of 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 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...of the other, and the sides about the equal angles reciprocally proportional, are equal. Let the triangles be so placed that the equal angles may be vertically... ## The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...other, and the sides about the equal angles reciprocally proportional, are equal. PROP. XV. THEOR. Equal triangles which have an angle of the one equal to an angle of the other, have the sides about the equal angles reciprocally proportional : and triangles which have an angle... 