 | Massachusetts - 1897 - 1382 pages
...GEOMETRY. Prove the following propositions : — 1. Two triangles are equal when two sides and the indndfd angle of one are equal to two sides and the included angle of the other. 2. If two parallels are cut by a secant line, the alternate interior angles are equal.... | |
 | Euclides - 1858 - 248 pages
...bisect a given rectilineal angle. DEMONSTRATION. — P. 4. Two triangles are equal in every respect when two sides and the included angle of one are equal to two sides and the included angle of the other triangle. EXP. CONS. DEM. Given the st.line AB ; it is required to bisect it. On AB make... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...BAC. For, BDC > BEG, EEC > BAC (53, 2). Hence, BDC > BAC (23, 20). 55. Proposition XVIII. — Theorem. Two triangles are equal if two sides and the included angle of tlie one are respectively equal to two sides and tlie included angle of the otlier. Let ABC and DEF... | |
 | George Anthony Hill - Geometry - 1880 - 332 pages
...with the same 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,... | |
 | George Anthony Hill - Geometry - 1888 - 200 pages
...determined if one part is given? 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,... | |
 | George Anthony Hill - Geometry - 1888 - 202 pages
...determined if one part is given ? 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,... | |
 | Education - 1893 - 640 pages
...other. 12. Construct triangle 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,... | |
 | John Henry Walsh - 1896 - 282 pages
...67. 68. From 66 and 67 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other, each to each ; and (6) when two angles and the included side of one are equal to two... | |
 | John Henry Walsh - 1895 - 296 pages
...57. 58. From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other, each to each ; and (Z>) when two angles and the included side of one are equal to two... | |
 | John Macnie - Geometry - 1895 - 386 pages
...Then since AB = A'C, (14) and AC = A'C, (Above) AB = AC. QED (Ax. 1) PROPOSITION' VIII. THKOJKEM. 66. Two triangles are equal if two sides and the included angle of the one are respectively equal to two sides and the included angle of the other. Given: In triangles... | |
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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... 
