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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 Geometry - Page 65
by Adrien Marie Legendre - 1841 - 235 pages
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The Encyclopedia Americana: A Library of Universal Knowledge, Volume 25

Encyclopedias and dictionaries - 1920 - 934 pages
...sides. Triangles which have their homologous sides proportional are similar. 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. Two triangles which have their sides parallel or perpendicular,...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 457 pages
...the sum of three given squares. PROPOSITION XIII. THEOREM 378. 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. Given A ABC and A'B'C',...
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The Encyclopedia Americana: A Library of Universal Knowledge, Volume 25

Encyclopedias and dictionaries - 1920
...sides. Triangles which have their homologous sides proportional are similar. 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. Two triangles which have their sides parallel or perpendicular,...
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Proceedings of the Edinburgh Mathematical Society, Volumes 38-41

Edinburgh Mathematical Society - Electronic journals - 1920
...theorem in similarity corresponding to the converse theorem (2) is the following : If two triangles have an angle of the one equal to an angle of the other and another pair of angles supplementary, then the sides opposite to the equal angles are proportional...
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Drill Book in Plane Geometry

Robert Remington Goff - 1922 - 136 pages
...altitudes. 330. Two triangles with equal altitudes are to each other as their bases. *331. 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. *332. Two similar triangles...
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Junior High School Mathematics: 1st-3d Book, Book 3, Part 2

Edson Homer Taylor, Fiske Allen - Mathematics - 1923
...right triangles having an acute angle of the one equal to an acute angle of the other. 3. They have one angle of the one equal to an angle of the other and the including sides proportional. 4. The three sides of one are proportional to the three sides of the...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 457 pages
...to the student.] PLANE GEOMETRY PROPOSITION XIII. THEOREM 378. 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. Given A ABC an4 A'B'C',...
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 169 pages
...similar, if: 1. They have two angles of one respectively equal to two angles of the other. 2. They have an angle of the one equal to an angle of the other and the including sides proportional. 3. The sides of one are respectively proportional to the sides of the...
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Annual Report of the Commissioners ..., Volume 48

1882
...8. Calculate the area of a regular octagon whose side is one inch. 8 marks. 9. Triangles which have an angle of the one equal to an angle of the other, and the sides about these angles reciprocally proportional, are equal. Prove this. 8 marks. 1 0. The perpendiculars from...
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