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" ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. "
Junior High School Mathematics ... - Page 68
by Edson Homer Taylor, Fiske Allen - 1923
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Plane Geometry

William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...44, 36, 28, and 20, measurements being in centimeters. PROPOSITION IV. THEOREM 337. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Given two triangles...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...to one half its perimeter multiplied by the radius of the inscribed circle. 498, Two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including the equal angles. 503. Two similar triangles...
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Plane Geometry

William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Modern - 1912 - 360 pages
...measurements being in centimeters. f? . J/r IJ t T' y, d ' i d PROPOSITION IV. THEOREM 337. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. c' zc Given...
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The Dublin University Calendar, Volume 1

Trinity College (Dublin, Ireland) - 1913 - 568 pages
...the angle ASC is 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...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 pages
...CQ. Ax. 9 Also ZC = Z C. Iden. .'. A .4BC and PQC are similar. 288 (Jf two A have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar.) .\CA:CP = AB:PQ; 282 that is, CA : C'A' = AB : PQ. Ax. 9 But CA : C'A' = AB :...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...rectangle inclose a rhombus. Ex. 1067. 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. 1068. Two rectangles are similar if two adjacent sides are proportional. Ex. 1069. Three times...
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Schultze and Sevenoak's Plane Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...rectangle inclose a rhombus. Ex. 1067. 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. 1068. Two rectangles are similar if two adjacent sides are proportional. Ex. 1069. Three times...
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Solid Geometry

Sophia Foster Richardson - Geometry, Solid - 1914 - 234 pages
...relation : (a) if they are mutually equiangular ; (6) if their corresponding sides are proportional ; (c) if they have an angle of one equal to an angle of the other and the including sides proportional. 249. Show that two plane polygons can be placed in the homothetic relation if their homologous angles...
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Constructive Text-book of Practical Mathematics, Volume 2

Horace Wilmer Marsh, Annie Griswold Fordyce Marsh - Mathematics - 1914 - 270 pages
...the point of division of the radius with the extremity of the chord. Prove that these two triangles have an angle of one equal to an angle of the other and the including sides proportional, and are therefore similar. The necessary proportion can be obtained by substituting the chord in the...
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Constructive Text-book of Practical Mathematics, Volume 3

Horace Wilmer Marsh - Mathematics - 1914 - 304 pages
...same size. 2. Mutually equiangular. (Theorem 3.) 3. Homologous sides proportional. (Theorem 4.) 4. One angle of one equal to an angle of the other and the including sides respectively proportional. (Theorem 5.) 5. Sides respectively parallel or perpendicular. (Theorem 6.)...
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