 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 Geometry - Page 63by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 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 and... | |
 | 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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...proportional DB is found : which was to be done.* PROP. XIV. THEOR. EQUAL parallelograms which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2.) parallelograms which have... | |
 | Euclides - 1840 - 192 pages
...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 that the equal angles may be vertically... | |
 | Euclides - 1840 - 82 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...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), and... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...(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,...about the equal angles proportional, are similar. In the triangles ABC, DEF, let the angles, C, F,be equal, and AC : CB : : c Fig. 74. DF : FE, then... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...proportional DB is found : which was to be done.* PROP. XIV. THEOR. — Equal parallelograms which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2) parallelograms which have an... | |
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