 | Isaac Sharpless - Geometry - 1879 - 282 pages
...the other, and the sides about (he equal angles proportional, the triangles will be similar. Let the triangles ABC, DEF have the angle A equal to the angle D, and a\soAB:AC::DE:DF; then will the triangles AB C, DEF be similar. / \ /~ \ Place D on A, and DE EFB c... | |
 | 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... | |
 | District of Columbia. Board of Education - 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... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...angle FMN = angle E. \ ^ ' QED THEOREM VII. 393. Two triangles having one angle of the one equal to one angle of the other, and the sides containing these angles proportional, are similar. Hypothesis. ABC and A'B'C', two triangles in which Angle C = angle C". V A' : C'B' :: CA : CB. Conclusion.... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...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... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...the ratio of AN to NB is the duplicate of the ratio of AM to MB. 2. If two triangles of equal area have an angle of the one equal to an angle of the other, prove that the sides about the equal angles are reciprocally proportional. 3. Shew how to divide a... | |
 | Mathematical association - 1883 - 86 pages
...two adjoining sides of the one respectively equal to two adjoining sides of the other, and likewise an angle of the one equal to an angle of the other; the parallelograms are identically equal. [By Superposition.] COR. Two rectangles are equal, if two... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 170 pages
...Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles...have the angle A equal to the angle D, and the sides AB, AC, proportional to the sides DE, DF. Then will these triangles be similar. Take AG equal to DE,... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...NAM equal to SB. Draw AO parallel to BC. ANC = ACN = CAO. ANC = CBA + BAN. Complete the proof. 24. 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 in- _ eluding the equal angles. See Theo. VII. BAC :... | |
 | Dalhousie University - 1888 - 212 pages
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles have an angle of the one equal to an angle of the other, and have their areas proportional to the squares of the side* opposite these equal angles, they must be... | |
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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. 
