 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 396by John H. Williams, Kenneth P. Williams - 1916 - 162 pagesFull view - About this book
 | Alan Sanders - Geometry - 1903 - 392 pages
...equally distant from AB and BC. Proof. Draw PF _L to AB. Lay off BE = BF and draw PE. A PBF and PBE have two sides and the included angle of one equal respectively to two sides and the included angle of the other, whence ZF = ZE and PF = PE. PE is therefore perpendicular to BC, and P is equally distant... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...are right angles. PROPOSITION XV. THEOREM 1126. On the same or equal spheres, triangles that have 1. Two sides and the included angle of one equal respectively to two sides and the included angle of the other; or '2. Two angles and the included side of one equal respectively to two angles and the... | |
 | William Schoch - Geometry - 1904 - 152 pages
...to make ABCA1 symmetrical with respect to BC? What parts may these be ? 3. Given two triangles, with two sides and the included angle of one equal respectively to two sides and the included angle of the other. Can you place them together so as to form a symmetrical quadrilateral ? Can you, then,... | |
 | Webster Wells - Geometry - 1908 - 329 pages
...angles and sides of its polar triangle. PROP. XV. THEOREM 554. If two spherical triangles on the same or equal spheres have two sides and the included angle...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... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...sides of its polar triangle. PROP. XV. THEOREM 554. If two spherical triangles on the same or eqval spheres have two sides and the included angle of one...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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...important tests for congruence of triangles. 32. First Test for Congruence of Triangles. 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 congruent. This may be shown by the following argument: BA Let ABC... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1911 - 208 pages
...parts must be arranged in the same order. SOLID GEOMETRY. 244. THEOKEM. Two spherical triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other are congruent, if the given parts are arranged in the same order, and symmetrical, if... | |
 | George William Evans - Mathematics - 1911 - 120 pages
...Let us take the proposition Euclid I, 4, to which I have previously referred : — If two triangles have two sides and the included angle of one equal respectively to the corresponding parts of the other, the triangles are congruent. Suppose a=x, b=y, and the angle... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...either its size or its shape. PROPOSITION II. THEOREM SECOND TRIANGLE CONGRUENCE 134. 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 congruent, (sas) Given the triangles ABC and DEF, in which AB equals... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...either its size or its shape. PROPOSITION II. THEOREM SECOND TRIANGLE CONGRUENCE 134. If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the otlier, the triangles are congruent, (sas) Given the triangles ABC and DEF, in which AB equals... | |
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