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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...
Elements of Plane Geometry: For the Use of Schools - Page 70
by Nicholas Tillinghast - 1844 - 96 pages
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## Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...triangles. Thus the general properties of triangles involve those of all figures. j THEOREM. / (I 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (fig. 122), and let Fig....
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## Elements of Geometry

Adrien Marie Legendre - 1825 - 570 pages
...properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an ungle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (fig. 122), and let Kig....
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## Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...their «ides, &c. QED PROPOSITION VI. THEOREM. 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 have those angles equal which subtend the homologous sides....
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## Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...their sides, &c. QED PROPOSITION VI. THEOREM. 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 have those angles equal which subtend the homologous sides,...
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## The Geometrical Companion, in which the Elements of Abstract Geometry are ...

George Darley - Geometry - 1828 - 190 pages
...proportional, are equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which have an angle of the one equal to an angle of the other. For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road...
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## Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 84 pages
...F, are equal; and so, if 'the angles at F had been supposed equal, the triangles would have had each angle of the one equal to an angle of the other, and the side CF lying between correspondent angles in each; whence also DF is equal to FE. Is this sufficiently...
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## Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 pages
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional. Thus if the angle A = A (fig. 45), and if AB : AD : : AC : AF,...
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## Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 218 pages
...suppress , BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles have an angle of the one equal to an angle of the other, their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take...
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## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...proportional, the triangles will be equiangular. If two triangles have,one angle of one triangle equal to one angle of the other, and the sides about the equal angles proportional, the triangles will be equiangular. Equal parallelograms, and also equal triangles, which have one angle...
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## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...side (r). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . »r. 14 5. Au angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining an;;!« of the same affection, or one of them a right...
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