 Two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other. In the triangles ABC and A'B'C', let AB be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'.  Elements of Plane and Solid Geometry - Page 44by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
 | William Chauvenet - Geometry - 1871 - 380 pages
...C = F,and BC = EF, there will follow A = D, AB = DE, and AC = DF. PROPOSITION XXII.— THEOREM. 80. Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. In the triangles ABC, DEF, let AB be equal to DE,... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...C = F, and BC = EF, there will follow A = D, AB = DE, &ndAC = DF. PROPOSITION XXII.— THEOREM. 80. Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. In the triangles ABC, DEF, let AB be equal to DE,... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...necessary, and they are generally enough, to determine the triangle. THREE SIDES EQUAL. 282. Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. Let the side BD be equal to AI, the side BC equal... | |
 | 1876 - 646 pages
...[NOTE. — State what text-book you have studied on the subject and to what extent.] 1. Prove that two triangles are equal when the three sides of the...equal respectively to the three sides of the other. 2. A straight line cannot intersect the circumference of a circle in more than two points. 3. Upon... | |
 | Olaus Henrici - Congruences (Geometry) - 1879 - 228 pages
...quadrilateral will be a kite if AC =AC and BC=BC (§ 172). Hence Theorem : Two triangles are congruent if the three sides of the one are equal respectively to the three sides of the other. § 187. A quadrilateral is also a kite if two adjacent sides are equal, and if the angle between them... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...point common to the two lines, namely, C'. .-. the two A coincide, and are equal in all respects. QED GEOMETRY. BOOK I. PROPOSITION XXV. THEOREM. 108. Two triangles are equal when the three sides of ; one are equal respectively to the three sides of the other. B B' In the triangles ABC and A' B' C',... | |
 | Charles Scott Venable - 1881 - 380 pages
...taking from the one side AD and from the other its equal, AC, we have BC > BD. PROPOSITION XII. THEOREM. Two triangles are equal, when the three sides of the one are equal to the three sides of the other, each to each. Let the side AB = DE, AC = DF, BC = EF ; then shall... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...point common to the two lines, namely, C". . - . the two A coincide, and are equal in all respects. QED GEOMETRY. BOOK I. PROPOSITION XXV. THEOREM. 108. Two...equal respectively to the three sides of the other. В В' In the trtangles ABC and A' B' C', let AB = A' B', AC = A'C', BC^B' C'. Wearetoprove Д A BC... | |
 | Harvard University - 1882 - 336 pages
...sides or angles of two triangles in order to be able to infer that the triangles are equal ? Prove that two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. 2. Two chords of a circle which intersect within... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...common to the two lines. THE ELEMENTS OF GEOMETRY. THEOREM IX. 129. Two triangles are congruent if the three sides of the one are equal respectively to the three sides of the other. HYPOTHESIS. Triangles ABC and LMN, having AB = LM, BC = MN, and CA = NL. CONCLUSION. A ABC ^ A LMN.... | |
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