 | Francis Cuthbertson - 1874 - 400 σελίδες
...respects; (i.5) .'. A FGH is equiangular to &ABC, Also, If two A s have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, then shall the A s be equiangular. B CG ff Let ABC, FGH be two A s, having iBAC=i GFH, and such that... | |
 | Aaron Schuyler - 1876 - 384 σελίδες
...proportionality of sides involve equality of angles. 230. Proposition XXI.— Theorem. Two triangles having an angle of the one equal to an angle of the other, and tlie including sides proportional, are similar. In the triangles, ABC, DEF, let A = D, and AB : DE... | |
 | 1876 - 646 σελίδες
...polygons. Prove that two triangles are similar when they are mutually equiangular. 2. Two triangles having 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. 3. To inscribe A circle... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 σελίδες
...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... | |
 | Richard Wormell - 1876 - 268 σελίδες
...demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then the sides which contain the angle of the first are the extremes of a proportion of which the sides... | |
 | Elias Loomis - 1877 - 458 σελίδες
...point D toward 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... | |
 | George Albert Wentworth - 1877 - 416 σελίδες
...BC* + Vb* + Ш2 = 4 + 4 ^V + 4 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 of the sides including the equal angles. Let the triangles ABC and... | |
 | 1877 - 678 σελίδες
...given equilateral and equiangular pentagon. 9. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous... | |
 | George Albert Wentworth - 1877 - 426 σελίδες
...Ж? + m? + DA2 = 4 2 + * 2 + 4 4 QED GEOMETRY. BOOK IV. PROPOSITION XIII. THEOREM. 341. Two triangles having an angle of the one equal to an angle of the oiher are to each other as the products of the sides including the equal angles. Д Let the triangles... | |
 | James McDowell - 1878 - 310 σελίδες
...form a rectangle, then shall the triangles be equiangular (VI. 5, 16) 54 81. If two triangles have an angle of the one equal to an angle of the other and the rectangle under the sides about the equal angles equal, a side of each triangle being taken to form... | |
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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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... 
