 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...similar (20) ; therefore BG:EH—AB:DE=AC:DF=BC:EF THEOREM X. 23, Two triangles having an angle of the one equal to an angle of the other, and the sides including these angles proportional, are similar. E D In the triangles ABC, DEF let t!:e angle A = D and AB :DE=AC :DF then the triangles... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...proportional. PROPOSITION VI.—THEOREM. 32. Two triangles are similar, when an angle of the one is equal to an angle of the other, and the sides including these angles are proporportional. In the triangles ABC, A'B'C', let * A> A = A', and AB AC A'B' A'C ' ' / """/ »... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...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 the angle... | |
 | George Anthony Hill - Physics - 1880 - 204 pages
...equiangular with respect to each other. (b) K they have their homologous sides proportional. (c) If they have an angle of one equal to an angle of the other,...and the sides including these angles proportional. (18) The perpendicular upon the hypothenuse of a right triangle from the vertex of the right angle,... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...— 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 AB:DE — AC:DF D then the triangles... | |
 | Cornell University - 1880 - 868 pages
...commensurable and incommensurable arcs. 4. Two triangles are similar, when an anj,rle of the one is equal to an angle- of the other and the sides including these angles are proportional. 5. To construct a triangle equivalent to a given polygon. 6. The circumferances of... | |
 | District of Columbia. Board of Education - Education - 1881 - 314 pages
...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 cut off equal to BC, and EF be drawn... | |
 | Great Britain. Education Department. Department of Science and Art - 1882 - 510 pages
...attached to the questions differ little from one another. 1. Two triangles which have an angle of the one equal to an angle of the other, and the sides including the equal angles proportional, are similar to each other. The straight line AB being produced to a... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...the triangles. PROPOSITION IV.— THEOREM. 20. Two triangles are similar when an angle of the one is equal to an angle of the other, and the sides including these angles are proportional. In the triangles ABC, A'B'C', let A = A', and AB AC . A'B' A'C' ' then these triangles... | |
 | Webster Wells - Algebra - 1890 - 560 pages
...similar, as also are the triangles EOG and COD ; for, by Geometry, two triangles are similar when they have an angle of one equal to an angle of the other, and the including sides proportional. Then the figure OFEG is similar to OBDC, and hence OFEG is a parallelogram.... | |
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... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. 
