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" If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal, respectively, to two sides and the included angle of the other, I. "
Solid Geometry - Page 396
by John H. Williams, Kenneth P. Williams - 1916 - 162 pages
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...hypothesis that angle «> angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 79. If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C' GIVEN — AB, AC, and a, of the triangle ABC respectively...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...equal, the figure is a rectangle. 46. Prove by coincidence that two parallelograms are equal if they have two sides and the included angle of one equal respectively to two sides and the included angle of the other. 42 PLANE GEOMETRY PROPOSITION XXVIII 109. Theorem. // two sides of a quadrilateral are...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 254 pages
...PROBLEM. To construct a square on a given side. PROPOSITION XXVI. THEOREM. 115. If two parallelograms have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the parallelograms are equal. 7 ».D *a FIG. 53. [Superpose, and use Ax. III.] 116. COR....
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 180 pages
...mutually equiangular. (The proof is left to the pupil ; compare § 600.) PROP. XXII. THEOREM. 602. If two spherical triangles on the same sphere, or equal...respectively, to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 196 pages
...mutually equiangular. (The proof is left to the pupil ; compare § 600.) PROP. XXII. THEOREM. 602. If two spherical triangles on the same sphere, or equal...the included angle of one equal, respectively, to ttvo sides and the included angle of the other, II. They are symmetrical if the equal parts occur in...
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Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...QEF Quod erat faciendum, wh ich was to be done. BOOK I PROPOSITION I. THEOREM 30. If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal in all respects. Let the A ABC and DEF have AB = DE, BC = EF,...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...7. THEOREMS ON THE EQUALITY OF TRIANGLES. Two triangles are identically equal if they have — (1) Two sides and the included angle of one equal, respectively, to two sides and the included angle of the other. § 41. (2) A side and the two adjacent angles of one equal, respectively, to a side and...
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Concrete Geometry: Introductory to Formal Plane Geometry

Theophilus Nelson - Geometry, Modern - 1902 - 154 pages
...triangles equal? What general principle may be inferred from this in regard to two triangles which have two sides and the included angle of one equal,...respectively, to two sides and the included angle of the other? Statement : — 101. Draw a triangle ABC with the sides AB, BC, and CA equal, respectively,...
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Plane Geometry by the Suggestive Method

John Alton Avery - Geometry, Modern - 1903 - 136 pages
...right angles, their exterior sides are in the same straight line. 29. Theorem VI. If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal. 32. Theorem VII. If two triangles have two angles and the included...
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Ellen: Or, Whisperings of an Old Pine, Volume 1

Joseph Battell - Force and energy - 1903 - 722 pages
...opposite the greater angle.' "Demonstrated under Figure i (Eighth). PROPOSITION XXII. 1 If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle oí the other, the triangles are equal.' "Because the third sides, extending over equal space, are...
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