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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 69
by Benjamin Peirce - 1836 - 71 pages
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...left 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 and A'B'C',...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...• 1 AA'B'C' AW Proof. Since the triangles are similar, Given 282 (The areas of two triangles that 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.) AABC AB AC AC (Similar...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...Const. CA:CP = CB:CQ. Ax. 9 Also ZC = ZC Iden. .'. A^J5C and PQC are'similar. 288 (If two A /iaue a?i angle of the one equal to an angle of the other, and the including sides proportional, they are similar.) a '.CA:CP = AB:PQ; 282 that is, CA : C'A' = AB :...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1914 - 284 pages
...inscribed in a circle is half that of the square oircumBCribed about the same circle. 8. Prove that if two triangles have an angle of the one equal to an angle of the other arxcl the sides about these angles proportional the triangles will be similar. 9. Two circles intersect...
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Plane Geometry

John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...equal to an acute angle of the other. PLANE GEOMETRY 410. THEOREM. Two triangles are similar, if they have an angle of the one equal to an angle of the other and the including sides are proportional. , FIG. 186. Given the A ABC and A'B'C', with ZA = Z A', and AB =...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...proportional to their corresponding sides. Suggestion. Apply Art. 220, Cor. 3. 222. Theorem XVI. // two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, the triangles are similar. Given the triangles ABC and AiBiCi with angle...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...proportional to their corresponding sides. Suggestion. Apply Art. 220, Cor. 3. 222. Theorem XVI. // two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, the triangles are similar. Given the triangles ABC and AiBiCi with angle...
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The Encyclopedia Americana: A Library of Universal Knowledge, Volume 25

Encyclopedias and dictionaries - 1920 - 934 pages
...its 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 - 486 pages
...to 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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Proceedings of the Edinburgh Mathematical Society, Volumes 38-41

Edinburgh Mathematical Society - Electronic journals - 1920 - 460 pages
...are collinear. The 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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