 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...  Elements of Plane and Solid Geometry - Σελίδα 146των George Albert Wentworth - 1877 - 398 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Euclides - 1874 - 342 σελίδες
...intercepted area, according as they intersect internally or externally. 15. If two trapeziums have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 σελίδες
...equal PKOP. XI— THEOREM. (Euc. VI. 14, 15.) Equal parallelograms and equal triangles, which have an angle of the one equal to an angle of the other, have their sides about the equal angles reciprocally proportional; and conversely. Let MB and BN be... | |
 | L J V. Gerard - 1874 - 428 σελίδες
...are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which have an angle of the one equal to an angle of the other, have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC... | |
 | Aaron Schuyler - 1876 - 384 σελίδες
...sides, nor does 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
...Define similar 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... | |
 | 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... | |
 | J. G - 1878 - 408 σελίδες
...contained between the point and the parallels. 14. // two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then tfie sides which contain Vie angle of the first are the extremes of a proportion of which the... | |
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