| Elias Loomis - Conic sections - 1877 - 458 pages
...the point D toward B, or from it. D2 PROPOSITION XXI. THEOREM. Two triangles are similar when they **have an angle of the one equal to an angle of the other, and the sides** including those angles proportional. Let the triangles ABC, DEF have the angle A of the one equal to... | |
| George Albert Wentworth - Geometry - 1877 - 436 pages
...EH AE = B'C'' A'B' B'C' =A'B', Hyp. Ax. 1 Cons. PROPOSITION VI. THEOREM. 284. Two triangles having **an angle of the one equal to an angle of the other, and the** including sides proportional, are similar. A A' In. the triangles ABC and A' B' С' let /А / Л1 *... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...4 ÊF* = AC1 + SD* + 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having **an angle of the one equal to an angle of the other** are to each other as the products cf t he sides including the equal angles. Let the triangles ABC and... | |
| James McDowell - 1878 - 310 pages
...triangle being taken to form a rectangle, then shall the triangles be equiangular (VI. 5, 16) 54 81. **If two triangles have an angle of the one equal to an angle of the other and the** rectangle under the sides about the equal angles equal, a side of each triangle being taken to form... | |
| William Henry Harrison Phillips, Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...ABD = ABF " (2, Cor. 3). ABE BE .. . ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. **If two triangles have an angle of the one equal to an angle of the other,** the ratio of their areas is equal to that of the products of the sides which contain those angles.... | |
| J. G - 1878 - 408 pages
...secant contained between the point and the parallels. 14. // two parallelograms are equal in area, and **have an angle of the one equal to an angle of the other,** then tfie sides which contain Vie angle of the first are the extremes of a proportion of which the... | |
| James Maurice Wilson - 1878 - 450 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise **an angle of the one equal to an angle of the other** ; the parallelograms are identically equal. Part. En. Let A BCD, EFGH be two parallelograms which have... | |
| Āryabhaṭa - 1878 - 100 pages
...equal (E. 1. 8). I PROP. xix. TIIEOIIEM. (E. 6. 14, 15). Equal triangles and parallelograms laving **an angle of the one, equal to an angle of the other,** have their sides about th« equal angles, reciprocally proportional. And conversely triangles and parallelograms... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...we have AB:AG — AC:AH But by hypothesis AB : D F.= AC : DF THEOREM XXIV. 60i Two triangles having **an angle of the one equal to an angle of the other, and the sides** including these angles proportional, are similar. In the triangles ABC, DBF let the angle A = D and... | |
| Education - 1881 - 314 pages
...TENTH GRADE. MAY itf. GEOMETRY AND TRIGONOMETRY. (Twenty credits.) 1. Theorem: — Two triangles having **an angle of the one equal to an angle of the other, and the sides** including these angles proportional, are similar. 2. If from the diagonal BD of a square ABCD, BE be... | |
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