| Webster Wells - Geometry - 1908 - 338 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, Modern - 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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