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 65by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| Charles Davies - Geometry - 1854 - 432 pages
...implication, those of all f1gures. BOOK IY. 109 D 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. Let ABC, DEF, be two triangles, having the angle... | |
| William Somerville Orr - Science - 1854
...other, have their sides about the equal angles reciprocally proportional ; and triangles which have **an angle of the one equal to an angle of the other, and** their sides about those angles reciprocally proportional, are equal to one another. Let the triangles... | |
| Euclides - 1855
...reciprocally proportional, they are equiangular. PROP. XV. ТНЕORЕМ. Equal triangles which have **an angle of the one equal to an angle of the other,** have their sides about the equal angles reciprocally proportional; and conversely, triangles which... | |
| Euclides - 1855
...angle of the other. If triangles are equiangular . If triangles are similar . . If equal triangles have **an angle of the one equal to an angle of the other.** If triangles have an angle in the one equal to an angle in the other, and their sides about the equal... | |
| George Roberts Perkins - Geometry - 1856 - 235 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have **an angle of the one equal to an angle of the other.** All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
| Peter Nicholson - Cabinetwork - 1856 - 216 pages
...the sum of the two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which have **an angle of the one equal to an angle of the other,** are to each other as the rectangle of the sides about the equal angles. Suppose the two triangles joined,... | |
| Euclides - 1859
...àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, laa iariv iKtlva. Equal triangles which have **an angle of the one equal to an angle of the other** have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle... | |
| Eucleides - 1860
...equal parallelograms have an angle of the one equal to an angle of the other. If parallelograms have **an angle of the one equal to an angle of the other, and** their sides about the equal angles reciprocally proportional. If parallelograms are about the diameter... | |
| George Roberts Perkins - Geometry - 1860 - 443 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have **an angle of the one equal to an angle of the other.** All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
| Benjamin Greenleaf - Geometry - 1862 - 490 pages
...by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have **an angle of the one equal to an angle of the other, and the sides** containing. these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A... | |
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