 | Euclid - 1868 - 138 pages
...oiher, have their sides about the equal angles reciprocally proportional ; and triangles which have an angle in the one equal to an angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another. PART I. Statement... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...varied at pleasure, without altering the lengths of the sides. THEOREM XVII. If two triangles have an angle in the one equal to an angle in the other, and the sides containing these angles proportionul,the \wo triangles will be equiangular and similar. Proportion... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...between Ul) iind DC. the two segments of the diameter; that is, AD!=BDxDC. PROPOSITION XXIII. THEOREM. Two triangles, having an angle in the one equal to an angle tn the other, are to each other as the rectangles of t 'ie sidtt which contain the equal angles. Let... | |
 | 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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...between BD and DC, the two segm'ents of the diameter ; that is, AD2=BDxDC. PROPOSITION XXIV. THEOREM. Two triangles, having an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides which contain the equal angles. Let the two triangles... | |
 | Horatio Nelson Robinson - Navigation - 1878 - 564 pages
...DII:DB = HG-.BE 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...proportional ; the two triangles are therefore equiangular (Geom. Cor. 2, Th. 17, B. II.) ; and they are similarly situated, for their sides make equal angles... | |
 | Eli Todd Tappan - Geometry - 1868 - 454 pages
...straight lines, those lines form a parallelogram. 7. Two parallelograms are similar when they have an angle in the one equal to an angle in the other, anj these equal angles included between proportional sides. MEASURE OF AREA. 377* The standard figure... | |
 | 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 triangles a side... | |
 | Elias Loomis - 1880 - 456 pages
...DC, the two segments of the diameter ; that is, AD2=BDxDC. PROPOSITION XXIV. THEOREM. Two triatigles, having an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides which co-retain the equal angles. Let the two triangles... | |
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Two triangles, having an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides which contain the equal angles. 
