| 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... | |
| 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.... | |
| 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°,... | |
| 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... | |
| 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... | |
| 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... | |
| 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 =... | |
| 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... | |
| 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... | |
| 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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