 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
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...+ DB < AC + CB. NOTE. — Have pupils give demonstration, prolonging BD instead of AD. THEOREM XII. 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, they are equal throughout. The... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...the adj. A equal, each Z is art. Z). PROPOSITION XLIV. THEOREM. 140. Two parallelograms, Aaving two sides and the included angle of the one equal respectively to two sitles and the included angle of the other, are equal in all respects. B СB' О A " D А' L4 In the... | |
 | William John M'Clelland - 1885 - 182 pages
...three given ares (any two of which being supposed greater than the third}. (Cf. Euc. I. xxii.) (7). 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 triangles are equal in every respect.... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...and bisect the angles of the rhombus. PROPOSITION XLI. THEOREM. 185. Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of thc- other, are equal. In the parallelograms ABCD and A'B'C'D', let AB = A'B', AD = A'D', and ZA=ZA'.... | |
 | George Albert Wentworth - Geometry - 1890 - 296 pages
...and bisect the angles of the rhombus. PROPOSITION XLII. THEOREM. 185. Two parallelograms, having two sides and the included, angle of the one equal respectively to two sides and the included angte of the other, are equal It C rf C" In the parallelograms ABCD and A'B'C'D ' , let AB = A'B',... | |
 | Euclid - Geometry - 1890 - 442 pages
...side BC = side YZ, side CA = side ZX ; and, finally, area ABC = area XYZ. Proposition 4. THEOREM — 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, then the triangles are identically... | |
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...TRIANGLES. SYNOPSIS.* SECTION I.— EQUAL TRIANGLES. 1O.>. i. DEFINITIONS. 2. PROPOSITIONS. PROP. I. 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, they are equal in all their parts.... | |
 | Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...opposite or vertical angles are equal. 4. If two angles have their sides parallel they are equal. 5. If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, they are equal in all their parts. If two triangles... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...equal to the given lines, and it is, therefore, the required triangle. PROPOSITION I. Theorem : // 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, they are equal in all their parts.... | |
 | William Benjamin Smith - Geometry, Modern - 1892 - 314 pages
...the symbol A. We now ask, When are 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£... | |
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