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" If two triangles have an angle of one equal to an angle of the other... "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 172
by Euclid, Rev. John Allen - 1822 - 494 pages
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Plane Geometry

William James Milne - Geometry, Plane - 1899 - 242 pages
...to their altitudes. 336 c. To the products of their bases by their altitudes. 336 d. If they have an angle of one equal to an angle of the other, to the products of the sides including the equal angles. 340 e. If they are similar triangles, to...
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SYLLABUS OF PROPOSITIONS IN GEOMETRY

1899
...respectively equal to two angles of the other, the triangles are similar. THEOREM III. If two triangles have an angle of one equal to an angle of the other and the sides including these angles proportional, the triangles are similar. THEOREM IV. If two triangles...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 473 pages
...polygon. PROPOSITION VII. THEOREM. ).-•. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to each other us the products of the sides including the equal angles. Let the triangles ABC and ADE have the common...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 218 pages
...of its bases multiplied by the altitude. 410. 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. 412. The areas of two similar polygons are...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 240 pages
...each other as the products of the sides including the supplementary angles. Ex. 540. If two triangles have an angle of one equal to an angle of the other, and a second angle of one supplementary to a second angle of the other, the sides about the third angles...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 370 pages
...three given squares. PROPOSITION XV. THEOREM 369. 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. D c A' D' Hyp. In triangles ABC and A'B'C',...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...three given squares. PROPOSITION XV. THEOREM 369. H4e 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. D A' D. G' Hyp. In triangles ABC and A'B'C',...
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Plane Geometry

Arthur Schultze - 1901
...three given squares. PROPOSITION XV. THEOREM 369. 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. D a B' A' D' Hyp. In triangles ABC and A'B'C',...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 440 pages
...equal, respectively, to two angles of the other, the triangles are similar. 250. (3) If two triangles have an angle of one equal to an angle of the other, and the sides including these angles proportional, the triangles are similar. 251. (4) If the ratios...
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Plane and Solid Geometry

Arthur Schultze - 1901
...three given squares. PROPOSITION XV. THEOREM 369. 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. B' ADC A' D' C' Hyp. In triangles ABC and...
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