 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
 | Education - 1902 - 880 pages
...the line that cuts off the greater distance is the longer. 2 Prove that two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. 3 Prove that lines which meet in a point intercept proportional segments on two parallel lines. 4 Complete... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...acute angle of ono are respectively equal to a side and an acute angle of the other. THEOREH XIX. 80. Two triangles are equal when the three sides of the...equal respectively to the three sides of the other. In the triangles ABC and DEF, let the side AB = DE, BC = EF, and CA = F D. To prove that the triangles... | |
 | John Charles Stone - Geometry - 1904 - 60 pages
...reductio ad absurdum. As an example of this, take the proposition that, Two triangles are congruent when the three sides of the one are equal respectively to the three sides of the other. In the other two cases of congruent triangles that text-books generally give before this one is taken... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...bisects the vertical angle of the triangle. PROPOSITION XXIV. THEOREM. 150. 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... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...with C. The same reasoning applies to A" B" C", after the latter triangle has been turned over. 75. Two triangles are equal when the three sides of the...equal, respectively, to the three sides of the other. C' FIG. 80 In Fig. 50, let A'B1, ffC', and C' A' be equal, respectively, to AB, BC, and CA. Place A'... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...included side of the one are equal respectively to two angles and the included side of the other ; 3 If the three sides of the one are equal respectively to the three sides of the other ; Provided that the equal parts in each case are arranged in the same order. PROOF In cases 1 and 2,... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...included side of the one are equal respectively to two angles and the included side of the other ; 3 If the three sides of the one are equal respectively to the three sides of the other ; Provided that the equal parts in each case are arranged in reverse order. PROOF In each case, A and... | |
 | Irving Elgar Miller - Thought and thinking - 1909 - 354 pages
...equals DC of II, by construction. Therefore triangle I equals triangle II. (Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other.) Therefore angle x equals angle y. (Homologous angles of equal triangles are equal.) QED Our study of... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...st. Z.) Since AC' = A'C', .-.AB' = A'B'. .'. AABCis congruent to A A'B'C'. ( Two A are congruent if the three sides of the one are equal respectively to the three sides of the other.) QED §85 §80 J EXERCISE 9 1. ABCD is a square and M is the raid-point of AB. With M as a center an... | |
 | David Eugene Smith - Geometry - 1911 - 370 pages
...but we do not know which is false, or if only one is false. THEOREM. Two triangles are congruent if the three sides of the one are equal respectively to the three sides of the other. It would be desirable to place this after the fourth proposition mentioned in this list if it could... | |
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