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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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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 470 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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Connecticut School Document, Issues 1-13

Education - 1913
...one If two triangles have their homologous sides proportional they are similar If two triangles have an angle of the one equal to an angle of the other their areas are to each other as the products of the sides including the equal angles The area of a...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 pages
...in. 31. 13 sq. ft, 9 ft., 5 ft. PROPOSITION VII. THEOREM 332. 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. •A. DB Given the triangles...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1913
...equal either to the angle AGP or to the angle ACQ. 7. Prove that if two triangles have an angle of one equal to an angle of the other, and the sides about these equal angles proportional, they are similar. 8. Prove that similar polygons can he divided up...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 457 pages
...solution is left to the student.] 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 product of the sides including the equal angles. Given A ABC and A'B'C', Z...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 304 pages
...solution is left to the student.] 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 product of the sides including the equal angles. Given A ABC and A'B'C', Z...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1914
...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 - 252 pages
...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. Given FIG. 186. the A ABC and A'B'C', with AB = AC A'C'' and A'B'...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...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, Plane - 1916 - 276 pages
...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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