If two sides and the included angle of one triangle are equal respectively to two sides and the included angle of another triangle, then the triangles are congruent. Solid Geometry - Page 296by Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - 1922 - 192 pagesFull view - About this book
| University of the State of New York - Education - 1868 - 160 pages
...demonstration is that which is given to the XXVI of Euclid, though usually stated in a different way, namely : "If two sides and the included angle of one triangle...respectively to two sides and the included angle of another triangle the two triangles are equal," &c. In this case the demonstration is purely geometrical, and... | |
| Paul Henry Hanus - Geometry - 1893 - 76 pages
...triangles are equal throughout. T. Put that into a single statement. Teacher obtains from P. : When two sides and the included angle of one triangle are equal respectively to two sides, etc. T. We can show that this must be true always, as follows. The general proof of the proposition... | |
| Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...Analysis. 1°. because e — e'. d is J_ c because & = V. 2°. b = b' Proof, e = e' because c = c' (if two sides and the included angle of one triangle are equal, etc.) . -. b = V, § 18. But if b = b' and c = c', then d is J_ to 'c. (If a straight line have two... | |
| Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...conclusion. Thus in Proposition I. we have: Hypothesis.—If two sides and the included angle of any triangle are equal, respectively, to two sides and the included angle of another triangle, conclusion, the triangles are equal. II. The Particular Enunciation, which refers to the... | |
| George F. Cole - 1909 - 368 pages
...them as to size? Are they equal? Why? From Problem B we learn that : Two triangles are equal when 2 sides and the included angle of one triangle are equal, respectively, to 2 sides and the included angle of the other. Draw two triangles as ABC and DEF with two sides and the... | |
| George William Myers - Mathematics - 1909 - 390 pages
...triangles are congruent. 292. We have thus far proved three theorems on congruent triangles, viz. : I. If two sides and the included angle of one triangle are equal, each to each, to two sides and the included angle of another triangle, the triangles are congruent.... | |
| George William Myers - Mathematics - 1910 - 304 pages
...congruency is ^. Thus, ABC = A'B'C' means ABC and A'B'C' may be made to coincide. PROPOSITION I 24. Theorem: If two sides and the included angle of one triangle...respectively, to two sides and the included angle of another triangle, the triangles are congruent. c ,, FIG. 14 Conclusion: Then the triangles ABC and A'B'C' are... | |
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