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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

Jacob William Albert Young, Lambert Lincoln Jackson - Geometry, Plane - 1916 - 328 pages
...are siruilar. Hence, show that DG . DE = DH • DF. PROPOSITION XIII. THEOREM 316. If two triangles have an angle of one equal to an angle of the other and the sides including these angles proportional, the triangles are similar. A 3 A' . O' Given A ABC and A'B'C',...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...The area of a trapezoid is equal to the product of its altitude and mid-line. 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. 344. In a right...
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...DExDF~lDE DF AB AC 5. DE DF AABC =AB A DEF DE* DE' Def. sim. A Ax. XII EXERCISES 1. Two triangles that have an angle of one equal to an angle of the other, have the sides including the equal angles 4 in. and 9 in. and 12 in. and 5 in., respectively. Compare...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...successively 54, 68, 72, 72, 60, 44, 36, 28, and 20, measurements being in centimeters. 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

Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...corresponding sides of two triangles are proportional, the triangles are similar. 310. If two triangles have an angle of one equal to an angle of the other, and the sides including these angles proportional, the triangles are similar. 312. If two polygons are similar,...
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Plane Geometry

Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...prove that the two triangles thus formed are similar. PROPOSITION VIII. THEOREM 310. If two triangles have an angle of one equal to an angle of the other, and the sides including these angles pro- . portioned, the triangles are similar. Given the A ABC and A'B'C',...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 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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Plane Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...between two segments * and y whose • difference is AB (see Fig. 434). FIG. 434 t34. If two triangles have an angle of one equal to an angle of the other, the ratio of the areas equals the ratio of the products of the sides that include the equal angles...
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Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...in the figure. Find the area of the cross section in square feet. 376. Theorem. Two triangles that 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. Given AABC and ADEF with...
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Solid Geometry

Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...a trapezoid equals the product of its altitude and its median. 375. Theorem. Two triangles that 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. 376. Theorem. The square...
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