 | 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 - 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... | |
 | 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... | |
 | 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 = £... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...to it at its mid-point. .... _ ' I PROPOSITION VI. THEOREM. 91. Two triangles are congruent if they have two sides and the, included angle of the one equal, respectively, to tioo sides and the included angle of the other. c' A ~ B A' B' Given the As ABC and A'B'C', in which... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...the sum of the other two, and greater than their difference. 91. Two triangles are congruent if they have two sides and the included angle of the one equal,...respectively, to two sides and the included angle of the other. 92. Two right triangles are congruent if the legs of the one are equal, respectively,... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...congruent, (asa) Second Law of Congruence. 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) Third Law of Congruence. If two triangles have the three sides of one equal respectively... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...congruent, (asa) Second Law of Congruence. 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) Third Law of Congruence. If two- triangles have the three sides of one equal respectively... | |
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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. 
