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" Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides... "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 94
by Dennis M'Curdy - 1846 - 138 pages
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Plane Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 336 pages
...1 minute. 60 minutes = 1 degree. 60" 60' = 1'. = 1. 28. Experiment. The two triangles ABC and GHK have an angle of one equal to an angle of the other. Are these two triangles equal? FIG. 3 The two triangles ABC and DEF have the three angles of one equal...
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Robbin's New Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1915 - 282 pages
...= ZB (67). .-. A AMN is similar to A ABC (303). QED PROPOSITION XXII. THEOREM 306. 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. D / \ BCEF Given : A...
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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 their...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...of similar triangles are proportional to any two corresponding sides. Theorem XVI. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Theorem XVII. If two triangles have...
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Plane Geometry

Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...of similar triangles are proportional to any two corresponding sides. Theorem XVI. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. Theorem XVII. If two triangles have...
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 298 pages
....,.Z.EDF=ZA,Z.DEF=ZB,ZF=ZC. Ax. I 12. .-.AABC~ADEF. Def.sim.poly. 130. Theorem. — If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, they are similar. C Hypothesis. In A ABC and A DEF, Z(7 = ZF...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...one equal respectively to the angles of the other, the triangles are similar. 386. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, the triangles are similar. 391. The homologous altitudes of two...
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Solid Geometry

John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...triangles have their corresponding sides proportional, the triangles are similar. 130. If two triangles have an angle of one equal to an angle of the other, and the including sides proportional, they are similar. 146. The sum of any two sides of a triangle...
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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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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...
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