 | Aaron Schuyler - Geometry - 1876 - 384 pages
...(358, 24), (451, 6), (453, 1). 457. Proposition XV. — Theorem. Two triangles on tlie same sphere or on equal spheres, having two sides and the included angle of one respectively equal to two sides and the included angle of the other, are either equal or symmetrical.... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...PROPOSITION XLIV. THEOREM. 140. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal in all respects. B СВ' С' A -------- DA, In the parallelograms AB С D and A' B' С' D', let... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...PROPOSITION XLIV. THEOREM. 140. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal in all respects. B CD О A DA' 111 the parallelograms AB С D and A' B' C' D', let AB = A'B',... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...the word symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal...sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the same order, as in DEF and... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...the word symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal...sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the same order, as in DBF and... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...and D'DC are equal, and their planes are parallel (§ 455). Then the parallelograms AB' and DC' have two sides and the included angle of one equal respectively to two sides and the included angle of the other. Therefore the faces AB' and DC' are equal (§ 123), and their planes are parallel. In... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...ABC would be reduced to one of its sides. Proposition 9. Theorem.* 709. Two triangles on the same, or on equal spheres, having two sides and the included...angle of the other, are either equal or equivalent. Hyp. Let ABC, DEF be two A s having the side AB = DE, the side AC = DF, and the ZA= ZD. CASE I. When... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...triangle ABC would be reduced to one of its Proposition 9. Theorem.* 7O9. Two triangles on the same, or on equal spheres, having two sides and the included angle of one equal respectively to iwo sides and the included angle of the other, are either equal or equivalent. Hyp. Let ABC, DEF be... | |
 | William Benjamin Smith - Geometry, Modern - 1892 - 314 pages
...two triangles congruent? 47. Theorem XIII. — Two A having two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent. The data are: Two A, ABC and A'£'C', having the three equalities, A£ = A'£'9 AC = A'C',... | |
 | William Benjamin Smith - Geometry, Modern - 1892 - 160 pages
...two triangles congruent ? 47. Theorem XIII. — Two A having two sides and the included angle of the one equal respectively to two sides and the included angle of the other are congruent. The data are: Two A, ABC and A'B'C, having the three equalities, AB = A'B', AC = A'C', 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. 
