 | George Albert Wentworth - 1877 - 416 sider
...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... | |
 | Elias Loomis - 1877 - 458 sider
...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... | |
 | James Maurice Wilson - 1878 - 450 sider
...THEOREM 29. If two parallelograms have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one...other ; the parallelograms are identically equal. Part. En. Let A BCD, EFGH be two parallelograms which have two adjoining sides AB, BC of the one equal... | |
 | William Henry Harrison Phillips - 1878 - 236 sider
...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. ELEMENTS... | |
 | James McDowell - 1878 - 310 sider
...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... | |
 | J. G - 1878 - 408 sider
...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... | |
 | Āryabhaṭa - 1878 - 100 sider
...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 - 1880 - 260 sider
...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... | |
 | District of Columbia. Board of Education - 1881 - 314 sider
...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... | |
 | George Albert Wentworth - 1881 - 266 sider
...squares on the diagonals. GEOMETRY. — BOOK IV. PROPOSITION XIII. THEOREM. 3-41. Two triangles having an angle of the one equal to an angle of the other are to each other an the products of the sides including the equal angles. Let the triangles ABC and... | |
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Assuming that 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... 
