 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 Geometry and Trigonometry - Side 86av Adrien Marie Legendre - 1836 - 359 siderUten tilgangsbegrensning - Om denne boken
 | Benjamin Greenleaf - 1873 - 202 sider
...with the triangle ABC; hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have an angle of the one equal...to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to the... | |
 | David Munn - 1873 - 160 sider
...perpendiculars on it from the opposite angles 42 VII. To find the area of any polygon 43 EXERCISES (4) 44 VIII. 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 47 IX. The areas of similar... | |
 | Benjamin Greenleaf - 1874 - 206 sider
...with the triangle ABC; hence the triangles DEF, ABC are also equiangular and similar. THEOREM XV. 208. Two triangles, which have an angle of the one equal...to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have the angle A equal to the... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 sider
...proved very briefly in the following manner, if the restriction imposed by Euclid be withdrawn : — Two triangles which have an angle of the one equal to an angle of the other, are to one another in the ratio compounded of the ratios of the sides about the equal angles. Let ABC... | |
 | L J V. Gerard - 1874 - 428 sider
...of homologous angles 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... | |
 | Euclides - 1874 - 342 sider
...of the 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... | |
 | Aaron Schuyler - 1876 - 384 sider
...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... | |
 | Richard Wormell - 1876 - 268 sider
...same 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... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 sider
...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... | |
 | 1876 - 646 sider
...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... | |
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