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" Two triangles are congruent if the three sides of one are equal to the three sides of the other. Fig. "
Elementary and Constructional Geometry - Page 55
by Edgar Hamilton Nichols - 1896 - 138 pages
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...included angles are equal; therefore (I. 7), DE is equal to GH. Lastly, in the triangles DKE, GLH, because the three sides of one are equal to the three sides of the other, the angles DKE, GLH are equal (I. 4) to each other; but these angles are the inclination of the planes...
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Class lessons on Euclid

Marianne Nops - 1882 - 278 pages
...in order to prove the next proposition. SUMMARY OP PROPOSITION VIII., THEOREM 5. If in two triangles the, three sides of one are equal to the three sides of the other each to each, the triangles are equal in all respects. Cons.— Nil. AAA Proof. — By superposition....
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A Treatise on Spherical Trigonometry: And Its Application to Geodesy and ...

John Casey - Spherical trigonometry - 1889 - 199 pages
...and the adjacent angles of one are equal to a side and the adjacent angles of the other. 3. When the three sides of one are equal to the three sides of the other. 4. When the three angles of one are equal to the three angles of the other. Fig. 8. Cases 1, 2,...
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Examination Papers for the Academic Year ...

Examinations - 1893 - 392 pages
...work logically, 1 Define scalene triangle, trapezium, sector, tangent line, secant. 5 2 Prove that two triangles are equal in all respects if the three sides of the one are respectively equal to the three sides of the other. 5 3 In a triangle ABC, the angle B...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...angles compare? 2. Under what conditions are two triangles equal ? Theorem. Two triangles are equal, if the three sides of one are equal to the three sides of the other, each to each. Data : Any two triangles, as ABC and DEF, in which AB - DE, AC = IiF, and BC = EF. To...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...angles compare? 2. Under what conditions are two triangles equal ? Theorem. Two triangles are equal, if the three sides of one are equal to the three sides of the other, each to each. D Data: Any two triangles, as ABC and DEF, in which AB = J>E, AC = DF, and BC = EF. To...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 396 pages
...angles compare? 2. Under what conditions are two triangles equal ? Theorem. Two triangles are equal, if the three sides of one are equal to the three sides of the oiher, each to each. Data: Any two triangles, as ABC and DEF, in which AB = DE, AC — DF, and BC =...
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School Science and Mathematics, Volume 21

Education - 1921 - 970 pages
...triangles in order to decide whether or not they arc equal?" The first guess is that they are equal if the three sides of one are equal to the three sides of the other. Evidently correct, for if I take three sticks I can make only one triangle from them. But in making...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...of Theorem VII by superposition. 2. Two spherical triangles are either congruent or sym. metrical> if the three sides of one are equal to the three sides of the other. 3. Show how Ex. 2 can be proved by means of Theorem XIV, Book VI. 4. The base angles of an isosceles...
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Foundations and Fundamental Concepts of Mathematics

Howard Whitley Eves - Mathematics - 1997 - 370 pages
...common base and having their other pairs of corresponding sides equaL 8. Two triangles are congruent if the three sides of one are equal to the three sides of the other. 9. To bisect a given angle. 10. To bisect a given straight line segment. 11. To erect a perpendicular...
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