 | George Albert Wentworth - 1877 - 442 σελίδες
...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 - 1877 - 416 σελίδες
...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 - 312 σελίδες
...DEF are equiangular (constr.), therefore ABC and DEF are also equiangular. QED 81. If two triangles have an angle of the one equal to an angle of the other, and the rectangles under the sides about the equal angles equal, a side of each triangle being taken to... | |
 | Wm. H. H. Phillips - 1878 - 236 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | 1881 - 314 σελίδες
...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 σελίδες
...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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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... 
