 | Webster Wells - Geometry - 1908 - 336 pages
...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 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... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...preceding pages, where the corresponding theorems, etc., occur. 216 THEOREMS ON RECTILINEAR FIGURES 79. If two triangles have two sides and the included angle of one respectively equal to the two sides and the included angle of the other, the triangles are congruent.... | |
 | 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,... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...Distinguish 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.... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1910 - 300 pages
...upon three important tests for congruence of triangles. 32. First Test for Congruence of Triangles. If two triangles have two sides and the included angle...included angle of the other, the triangles are congruent. This may be shown by the following argument: BA Let ABC and A'ffC be two triangles in which AB = A'ff,... | |
 | 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
...more satisfactory. 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... | |
 | Geometry, Plane - 1911 - 192 pages
...vertex, divide one another in extreme and mean ratio. JUNE, 1905 (One hour and a half.) 1. Prove that if two triangles have two sides and the included angle of one respectively equal to two sides and the included angle of the other, the triangles are equal. Let ABC... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...without changing either its size or its shape. PROPOSITION II. THEOREM SECOND TRIANGLE CONGRUENCE 134. If two triangles have two sides and the included angle...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... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...adjoining angles of one equal respectively to a side and the two adjoining angles of the other. sas, having two sides and the included angle of one equal respectively to two sides and the included angle of the other. sss, having three sides of one equal respectively to three sides of the other. rt. A,... | |
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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. 
