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" THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side... "
Elements of Geometry: With, Practical Applications - Page 276
by George Roberts Perkins - 1850 - 320 pages
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...•'• A2t8C== AA 'B'C' for they can be made to coincide. Therefore, Two triangles are congruent if two angles and the included side of the one are equal to two angles and the included side respectively of the other. 67. APPLICATION OP PROPOSITIONS I AND II. If two triangles are congruent...
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Proceedings of the Annual Session

Arkansas Education Association - Education - 1912
...included angle of the other," or that "Two triangles are equal if two angles and the included side of one are equal to two angles and the included side of the other;" and to any other theorem which yields to this method. If the pupil is to prove that "In any isosceles...
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First Book in General Mathematics

Mathematics - 1917 - 284 pages
...and BC, being equal, are each marked with two cross lines. 76. Theorem : Two triangles are equal if two angles and the included side of the one are equal to two angles and the included of the other. Given: In A ABC and DEF, BC = EF, ZB = ZE, and ZC = Z F. To Prove: A ABC = A DBF. Proof:...
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Solid Geometry, with Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1919 - 240 pages
...of the other. See the figure SOLID GEOMETRY: BOOK V TRIANGLES EQUAL OR SYMMETRICAL 329. THEOREM XII. Two triangles on the same sphere, or on equal spheres, are equal or symmetrical if two sides and the included angle of one are equal respectively to two sides and the...
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Solid Geometry, with Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1919 - 232 pages
...of a triangle symmetrical to the given triangle. The proof is left for the student. 328. THEOREM XI. Two triangles on the same sphere, or on equal spheres, are equal or symmetrical if three sides of one are equal respectively to three sides of the other. SOLID GEOMETRY:...
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Modern Mathematics: Seventh-[eighth] Year, Volume 2

Raleigh Schorling, John Roscoe Clark - Mathematics - 1925 - 332 pages
...draw two congruent triangles, if we see to it that two angles and the included side of one triangle are equal to two angles and the included side of the other triangle. 7. Two Boy Scouts wished to know how far a target at T across a small lake was from their...
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...a. two sides and the included angle of the one are equal to the corresponding parts of the other; b. two angles and the included side of the one are equal to the corresponding parts of the other; c. they are mutually equilateral; d. they are mutually equiangular....
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Foundations and Fundamental Concepts of Mathematics

Howard Whitley Eves - Mathematics - 1997 - 370 pages
...from shore by using the fact that two triangles are congruent if two angles and the included side of one are equal to two angles and the included side of the other. Thomas L. Heath, the historian, has conjectured that this computation was probably made by an instrument...
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First Steps for Math Olympians: Using the American Mathematics Competitions

J. Douglas Faires - Mathematics - 2006 - 346 pages
...congruence by Side-Angle-Side. (SAS) Two triangles are congruent if two angles and an included side of one are equal to two angles and the included side of the other. This is called congruence by Angle-Side-Angle. (ASA) DEFINITION 5 A median of a triangle is a line...
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The Journal of Speculative Philosophy, Volume 11; Volume 19

Electronic journals - 1885 - 456 pages
...we cannot know by a single intuition. For instance; two triangles lie before me, and I am told that two angles and the included side of the one are equal to the two angles and the included side of the other ; and I am further told that, such being the case,...
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