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" Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. "
The Elements of geometry; or, The first six books, with the eleventh and ... - Page 143
by Euclides - 1855
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...respectively, to two angles of the other. PROPOSITION XVIII. THEOREM. 368. Two triangles are similar if they have an angle of the one equal to an angle of the other and the including sides proportional. EF Given As ABC and DBF in which XA = XD, and — = — . DE...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...one are equal respectively to two angles of the other. PROPOSITION XIV. THEOREM 288. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. ABA B' Given the triangles ABC and A'B'C',...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...triangles ACD and EBC that AC- BC = CE- CD. 430. EXERCISES. 1. The areas of two parallelograms having an angle of the one equal to an angle of the other are in the same ratio as the product of the sides including the equal angles. 2. Three semicircles of equal...
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...triangles ACD and EBC that AC- BC= CE- CD. 430. EXERCISES. 1. The areas of two parallelograms having an angle of the one equal to an angle of the other are in the same ratio as the product of the sides including the equal angles. 2. Three semicircles of equal...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 360 pages
...working only with the tape, is given on page 99. THE TEACHING OF GEOMETRY THEOREM. 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. This proposition may be omitted...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...Construct a circle equivalent to the sum of two given circles. Ex. 1125. Assuming that 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, prove that the bisector of an angle...
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Elementary Trigonometry

William Ernst Paterson - Logarithms - 1911 - 262 pages
...each, and a side of the one equal to the corresponding side of the other. Prop. 9. If two triangles have an angle of the one equal to an angle of the other, and the sides about another pair of angles equal, each to each, then the third angles are either equal...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...parts of equal area? (6) Trisect a right angle, and explain your construction. 6. If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, prove that the two triangles are similar. 6. The angle of a sector...
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Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Modern - 1911 - 266 pages
...of an inscribed rectangle enclose a rhombus. Ex. 737. Two parallelograms are similar when they'have an angle of the one equal to an angle of the other, and the including sides proportional. Ex. 738. Two rectangles are similar if two adjacent sides are...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...[The solution is 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', ZA = Z...
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