 Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.  The Elements of Solid Geometry - Page 94by William C. Bartol - 1893 - 95 pagesFull view - About this book
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...equal is used. For symbols see page vi . PROPOSITION II. THEOREM 68. Two triangles are congruent if two sides and the included angle of the one are equal respectively to tivo sides and the included angle of the other. AB x Y Given the triangles ABC and XYZ, with AB equal... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...two A.) .'. AA OP is congruent to A BOP. § 68 (Two A are congruent if two sides and the included Z of the one are equal respectively to two sides and the included / of the other.) .-.PA=PB, and' Z.APO = Z.OPB. §67 PROPOSITION X. THEOREM 84. Of two lines drawn from... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...corresponding side of the other. §184 PLANE GEOMETRY 191. THEOREM. Two triangles are congruent if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other. FIG. 76. Given To prove Proof. 1. 2. 3. 4. 5. the A ABC and A'B'C' with side AB = side... | |
 | Mathematics - 1915 - 830 pages
...as (2). 5. If equals are added to equals the sums are equal. 6. Two triangles are congruent if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other. 7. Equals may be substituted for equals in an equation. I would like to call particular... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...the student complete the proof.) 262. COROLLARY 1. Two parallelograms are congruent if two adjacent sides and the included angle of the one are equal, respectively, to two adjacent sides and the included angle of the other. 263. COROLLARY 2. Two rectangles are congruent... | |
 | Norwood Press - Printers - 1916 - 470 pages
...X. Two triangles on the same sphere, or on equal spheres, are either congruent or symmetric, if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other. Fio. 252 (a) Flo. 252 (6) Given the spherical A ABC and A'B'C1 on the same sphere or... | |
 | Ben DeKalbe Wood - Education, Higher - 1923 - 360 pages
...DIRECTIONS FOR SECTION X: Choose the easiest one first. 1. Prove: Two triangles are congruent if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other. 2. Prove: Two right triangles are congruent if the hypothenuse and a side of the one... | |
 | Ray Harbaugh Dotterer - Logic - 1924 - 364 pages
...1.13131.—Alternate-interior angles are equal. (See 1.1222.) 1.13132.—Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other. 1.131321.—The possibility of constructing the figure. (Postulate.) 1.131322.—Two... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1923 - 414 pages
...B Fio. 72 Since the proof is easily 88. Theorem XXIII. Two parallelograms are congruent if two Men and the included angle of the one are equal respectively to two aide* and the included angle of the other. Fio. 73 Given tho HIABCD and A'B'C'D' in which AB = A'B',... | |
 | Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...parallel through the vertex opposite. Proposition XXX. Theorem 92. Two triangles are equal, if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other. (Included angle acute.) B B' E' Hints: Prove the right triangles ABE and A'B'E' equal,... | |
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