 If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.  Mathematics, mechanics, heat - Page 21by American School (Chicago, Ill.) - 1903Full view - About this book
 | Cora Lenore Williams - Geometry - 1905 - 56 pages
...triangle; of four angles, a tetragon; of five angles, a pentagon; of six, a hexagon; etc. Theor. B. If two triangles have two sides and the included angle...two sides and the included angle of the other, the triangles are congruent. (If the sides of one triangle are arranged in reverse order to the corresponding... | |
 | David Sands Wright - Geometry - 1906 - 104 pages
...to test the equality or similarity of its parts. It is illustrated in the following demonstration : If two triangles have two sides and the included angle...two sides and the included angle of the other, the triangles are equal. Given the triangles ABC and DEF, having, respectively, the side AB = the side... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...these conclusions contradict the hypothesis that BC = EF. .-. ZA =Z D. .-. A ABC = A DEF, " having two sides and the included angle of the one equal respectively to two sides and the included angle of the other." § 162 QED EXERCISES 54 ABC and DBC are two isosceles triangles on the same base BC.... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...conclusions contradict the hypothesis that BC = EF. .-. ZA =Z D. .-. A ABC = A DEF, •' having two sides and the included angle of the one equal respectively to two sides and the included angle of the other." § 162 QED EXERCISES 54 ABC and DEC are two isosceles triangles on the same base BC.... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...between the terms "proposition," "theorem," " problem." SECTION VIII. TRIANGLE THEOREMS 92. Theorem I. If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the triangles are congruent. ANALYSIS... | |
 | Ernst Rudolph Breslich - Mathematics - 1909 - 402 pages
...following theorem: 274. Theorem: Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. The truth of this statement may be established by reasoning as follows: Let ABC and C A,BrC,, Fig. 186,... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 304 pages
...51). Also Z CEA = Z BEF. (Vertical angles are equal, § 74.) .-. A ACE Si A FBE. (Two triangles which have two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent, § 32.) .-. ZC= Z FBE. (Being angles opposite equal sides in congruent... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...51). Also Z CEA = Z BEF. (Vertical angles are equal, § 74.) .'. A ACE 21 A FBE. (Two triangles which have two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent, § 32.) .-. ZC = Z FBE. (Being angles opposite equal sides in congruent... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...through the same point. PROPOSITION VI. THEOREM. 91. Two triangles are congruent if they have tivo sides and the included angle of the one equal, respectively, to two sides and the included angle of the other. A " B A' B Given the As ABC and A'B'C', in which AB = A'B', AC = A'C', and £ A = £... | |
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