 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...segments of the base (59) are AE and CE. (I. 17.) (1. 45.) (16.) 61 i Two triangles having an angle of the one equal to an angle in the other are to each other as the rectangles of the sides containing the equal angles ; or ABC:ADE—ABXAC:AD X AE Draw BE. (13.) (Pn. 24.) (Pn. 21.) 62. Prove... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...sides, .nnd parallel to them, will be equal. 10. To construct a square, having a given diagonal. 11. Two triangles having an angle in the one equal to an angle in the other, have their areas in the ratio of the products of the sides including the equal angles. 12. If, of the... | |
 | Euclid - Geometry - 1872 - 284 pages
...equal to GC (by Prop. 15, B. 5). PROPOSITION XV. THEOREM. Of equal triangles (ABD and CBL), having also an angle in the one equal to an angle in the other, the sides about the equal angles are reciprocally proportional (AB to BC as LB to BD). And if two triangles... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...are equiangular and similar. PROPOSITION XHT.—THEOREM. Two triangles having an angle in each equal, are to each other as the rectangles of the sides which contain the equal angles. Let the two tri- T /V angles ABC and DEF have the angles C and F equal; / \ &/ then will ABC be to DEF as AC x... | |
 | Horatio Nelson Robinson - Navigation - 1878 - 564 pages
...And, DH :DB = HC:BF Therefore, IIG : BE = EC : BF($\i. 6, B. II.), Or, HG'.HO = BE:BF. Here, then, are two triangles, having an angle in the one equal to an angle in the other, and the sides about the equal angles proportional ; the two triangles are therefore equiangular (Geom.... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...both obtuse, the triangles are similar. Compare I. 96 - 100. 116. Two triangles having an angle of the one equal to an angle in the other are to each other as the rectangles of the sides containing the equal angles ; or (Fig. Art. 50) Draw D C. (47 ; 24 ; 21.) 117. Prove Theorem XXVIL,... | |
 | Robert Fowler Leighton - 1880 - 428 pages
...opposite the second. State and prove the converse. 3. Define similar polygons. If two triangles have an angle in the one equal to an angle in the other and the sides about these angles proportional, the triangles are similar. Prove. 4. If in two similar... | |
 | George Albert Wentworth - 1884 - 264 pages
...COMPARISON OP AREAS. 187. Theorem. The areas of two triangles having an angle of one equal to an angle of the other are to each other as the rectangles of the sides including the equal angles. 188. Theorem. Similar triangles are to each other as the squares upon the... | |
 | Dalhousie University - 1888 - 212 pages
...which meet in Q, the lines drawn from Q to all the other angles bisect them. 7. If two triangles have an angle in the one equal to an angle in the other, and the sides about these equal angles proportional, then must the triangles be similar. 8. If two... | |
 | George Albert Wentworth - 1889 - 264 pages
...COMPARISON OF AREAS. 187. Theorem. The areas of two triangles having an angle of one equal to an angle of the other are to each other as the rectangles of the sides including the equal angles. 188. Theorem. Similar triangles are to each other as the squares upon the... | |
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Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig. 128. which contain the equal angles; thus the triangle ABC (fig. 
