 If two triangles have the three sides of one equal respectively to the three sides of the other, the triangles are congruent, (sss) REMARK 1.  Solid Geometry - Page 451by George C. Shutts - 1913Full view - About this book
 | Education - 1902 - 730 pages
...side of B to the third side of A. Therefore the third sides of B and C arc equal, and B and C have the three sides of one equal respectively to the three sides of the other. Therefore the triangles B and C are congruent. But the angles of C equal respectively the corresponding... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...are either equal or symmetrical. Let ABC and D EF be two spherical triangles on the same sphere, or equal spheres, having the three sides of one equal respectively to the three sides of the other. To prove that ABC and DEF are either equal or symmetrical. SUG. 1. Connect the vertices of each A with... | |
 | Michigan Schoolmasters' Club - Education - 1894 - 554 pages
...congruent triangles, 2. parallelograms, etc. (a) To prove the triangles congruent requires that we have 1. The three sides of one equal, respectively, to the three sides of the other, 2. two angles and a side of one equal, respectively, to two angles and a side of the other, or 3. an... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...adjacent angles of one equal, respectively, to a side and the two adjacent angles of the other. § 43. (3) The three sides of one equal, respectively, to the three sides of the other. § 53. (4) Each a right angle, and the hypotenuse and a side of one equal, (5) Two sides of one equal,... | |
 | Michigan Schoolmasters' Club - Education - 1902 - 240 pages
...congruent triangles, 2. parallelograms, etc. (a) To prove the triangles congruent requires that we have 1. The three sides of one equal, respectively, to the three sides of the other, 2. two angles and a side of one equal, respectively, to two angles and a side of the other, or 3. an... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...the included side of one equal respectively to two angles and the included side of the other; or 3. Three sides of one equal respectively to the three sides of the other; Have their remaining parts equal, and the triangles are either equal or symmetrical. Proof. Draw radii... | |
 | John Charles Stone - Geometry - 1904 - 60 pages
...congruent triangles, 2. parallelograms, etc. (a) To prove the triangles congruent requires that we have, 1. the three sides of one equal, respectively, to. the three sides of the other. 2. two angles and a side of one equal, respectively, to two angles and a side of the other, or 3. an... | |
 | George Clinton Shutts - 1905 - 260 pages
...so that AC crosses OM, and prove the proposition. _^ PROPOSITION XIII. 89. Theorem. Two triangles, having the three sides of one equal, respectively, to the three sides of the other, are equal in all respects. AD A Let ABC and DBF represent two triangles, having AB equal to DE, AC equal... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...271. Theorem XI. (a) Two triangles on the same sphere are either congruent or symmetric if they have the three sides of one equal respectively to the three sides of the other. (6) Two trihedral angles are either congruent or symmetric if they have the three face angles of one... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 204 pages
...line which is farther from the perpendicular is the longer. 105. Theorem VII. // two triangles have three sides of one equal respectively to the three sides of the other, the triangles are congruent. Will superposition work ? If not, what other methods of proving triangles... | |
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