 | William Chauvenet - Geometry - 1871 - 380 pages
...face angles of the other. j^- -if " PROPOSITION XIX.— THEOREM. 72. Two triangles on the same sphere are either equal or symmetrical, when two sides and the included angle of one are respectively equal to two sides and the included angle of the other. In the triangles ABC and DEF,... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...opposite face angles of the other. PROPOSITION XIX.— THEOREM. 72. Two triangles on the same sphere are either equal or symmetrical, when two sides and the included angle of one are respectively equal to two sides and the included angle of the other. In the triangles ABC and DEF,... | |
 | George Anthony Hill - Geometry - 1880 - 332 pages
...given parts, and prove that it is equal to the first. Theorem. — Two parallelograms are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other. Exercises. — 1. Construct a parallelogram, the two sides being 44cm and 66cm, and the... | |
 | Cornell University - 1880 - 868 pages
...parallelepipeds having equal altitudes are to each other as their bases. 3. Two triangles on the same sphere are either equal or symmetrical when two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. 4. A frustum of any... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...theorem gives the following relations: PROPOSITION XII.—THEOEEM. 53. Two triangles on the same sphere are either equal or symmetrical, when two sides and the included angle of one are respectively equal to two sides and the included angle of the other, In the triangles ABC and DEF,... | |
 | George Anthony Hill - Geometry - 1888 - 202 pages
...If two parts are given? If the three angles are given? 14. Theorem. — Two triangles are equal, if two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other. HYPOTHESIS. A ABC and DEF, AB=DE, AC=DF, CONCLUSION. -^ BDE A ABC = A DEF. FI°- 67PROOF.... | |
 | George Anthony Hill - Geometry - 1888 - 200 pages
...two parts are given ? If the three angles are given ? 14. Theorem. — Two triangles are equal, if two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other, HYPOTHESIS. A ABC and DEF, AB=DE, AC=DF, CONCLUSION. _ BDE A ABC = A DEF. ***- 67> PROOF.... | |
 | Education - 1893 - 640 pages
...by measuring two sides and included angle of a given triangle. Theorem: Two triangles are equal if two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other. 13. Theorem: i. In an isosceles triangle, the angles opposite the equal sides are equal.... | |
 | William Chauvenet - 1893 - 340 pages
...theorem gives the following relations: PROPOSITION XII.—THEOREM. 53. Two triangles on the same sphere are either equal or symmetrical, when two sides and the included angle of one are respectively equal to two sides and the included angle of the other. In the triangles ABC and DBF,... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...which is not in the right bisector of a straight line is unequally distant from the ends of the line. and the included angle of one are equal respectively to two sides and the included angle of the other. 146. Theorem. Two triangles are equal if two angles and a side of one are equal respectively... | |
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Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other... 
