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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

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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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 218 pages
...products of their bases by their altitudes. 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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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 358 pages
...Similarly, it may be proved that B"C" = B'C'. Two sides and included angle. 44. THEOREM 10. If two triangles have an angle of one equal to an angle of the other, and the sides about these angles proportional, then the triangles are similar. Let the triangles ABC...
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Plane Geometry by the Suggestive Method

John Alton Avery - Geometry, Plane - 1903 - 122 pages
...triangle, a smaller triangle is formed similar to the given triangle. THEOREM V 164. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Hyp. In the A RST and R'S'T', let...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903
...A', and ^^_ = — — A. 1 1 ./Y li Therefore the triangles ABE and A' B' E' are similar, for they have an angle of one equal to an angle of the other, and the sides including these angles proportional (Theorem LIII). Again, since the polygons are similar,...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 206 pages
...326. // two triangles have their homologous sides proportional they are similar. 327. // two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. 328. // two triangles have their sides...
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 372 pages
...is similar to A ABC). Art. 306. Art. 101. Ax. 8. QED PROPOSITION XVII. THEOREM 327. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Given the A ABC and A'B'C', in which...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 473 pages
...AREAS OF POLYGONS. 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 as the products of the sides including the equal angles. Let the triangles ABC and ADE have the common...
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