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" There are three important theorems in geometry stating the conditions under which two triangles are congruent: 1. Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the... "
Plane Geometry - Page 72
by John Charles Stone, James Franklin Millis - 1916 - 278 pages
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Plane Geometry

Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Modern - 1920 - 328 pages
...of the first. For example, the converse of Theorem 1 is as follows : If two triangles are congruent, two sides and the included angle of one are equal respectively to two sides and the included angle of the other. EXERCISES 18. State the hypotheses of Theorems 1 to 10 inclusive. State the conclusions....
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Bulletin, Issues 25-53

United States. Office of Education - 1921 - 1286 pages
...entire freedom in state-, ment and sequence. A. THEO It EMS. 1. Two triangles are congruent if ' (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other; (o) two angles and a side of one are equal, respectively, to two angles and the corresponding...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...or on equal spheres, two spherical triangles are either congruent or symmetrical and equivalent when two sides and the included angle of one are equal respectively to two sides and the included angle of the other. Use a method similar to that used in Prop. 332. Proposition 334 Theorem On the same sphere,...
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Bulletin

Education - 1921 - 1190 pages
...favors entire freedom in statement and sequence. A. THEOREMS. 1. Two triangles are congruent if ' (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other; (l>) two angles and a side of one are equal, respectively, to two angles and tlie corresponding...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...the included angle equal to x. NOTE. The construction and proof are to be given by the student. 164. Theorem. Two parallelograms are congruent if two sides...equal respectively to two sides and the included angle of the other. FIG. 179 Given the parallelograms ABCD and A'B'C'D', with AB equal to A'B', AD equal...
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The Reorganization of Mathematics in Secondary Education

National Committee on Mathematical Requirements - Mathematics - 1922 - 84 pages
...favors entire freedom in statement and sequence. A. THEOREMS. 1. Two triangles are congruent if 1 (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other; (6) two angles and a side of one are equal, respectively, to two angles and the corresponding...
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Solid Geometry

Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...intersection of the diagonals of a parallelogram is the center of symmetry of the parallelogram. THEOREM 35. Two parallelograms are congruent if two sides and the included angle of one are equal to two sides and the included angle of the other. THEOREM 36. If a quadrilateral has one side equal...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...the sup. of Z 4, and £DE is a st. line. A ABD =s A CBD. PROPOSITION III. THEOREM 69. Two triangles are congruent if two sides and the included angle...equal respectively to two sides and the included angle of the other (sas = sas). Given A ABC and A'B'C' with AB = A'B', BC=B'C', and B = ZB'. To prove A ABC...
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An Introduction to Reflective Thinking

Laurence Ladd Buermeyer, Laurence Buermeyer - Thought and thinking - 1923 - 372 pages
...= BD, by definition of a square. Hence triangle FBC = triangle ABD, because two triangles are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. Because the angles GAB and BAG are both right angles, GA and AC are in the same straight...
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Plane Geometry: (Revised)

Claude Irwin Palmer, Daniel Pomeroy Taylor, Eva Crane Farnum - Geometry, Modern - 1924 - 360 pages
...experiment can be stated as a theorem, and proved by actual superposition. *56. Theorem. Two triangles are congruent if two sides and the included angle...equal respectively to two sides and the included angle of the other. Given the &ABC and DEF with AC = DF, AB = DE, and ZA = ZD. (Use Fig. 1 and Fig. 3, §...
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