 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...adjacent angles of one are equal respectively to a side and the two adjacent angles of the other. III. If the three sides of one are equal respectively to the three sides of the other. Provided in each case that the parts given equal are arranged in opposite order in the two triangles.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...adjacent angles of one are equal respectively to a side and the two adjacent angles of the other. III. If the three sides of one are equal respectively to the three sides of the other. Provided in each case that the parts given equal are arranged in the same order in both triangles.... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...AB=CD &n To Prove ABCD a O. Proof. Draw diagonal AC. In A ABC and ACD, AC = AC. And by hyp., AB=CD and BC = AD. .: A ABC = A ACD. [Two A are equal when...lines are cut by a transversal, and the alt. int. A are equal, the two lines are ||.] (§ 73) In like manner, since Z BAC = Z ACD, AB II CD. Then by... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...AB=CD &n To Prove ABCD a O. Proof. Draw diagonal AC. In A ABC and ACD, AC = AC. And by hyp., AB=CD and BC = AD. .-. A ABC = A ACD. [Two A are equal when...[In equal figures, the homologous parts are equal.] (§ 60) Since Z BCA = Z CAD, BC II AD. [If two str. lines are cut by a transversal, and the alt. int.... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...of triangle DEF is equal to AB ? which side is equal to BC? PROP. XVII. THEOREM. 69. 2^oo triangles are equal when the three sides of one are equal respectively to the three sides of the other. C Given, in &ABC and DEF, r> AB = DE, BC = EF, and CA = FD. To Prove A ABC = A DEF. Proof. Place A... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...of a str. line, any point in the _L is equally distant from the extremities of the line.] (§ 41, I) [Two A are equal when the three sides of one are equal...respectively to the three sides of the other.] (§ 69) Now revolve A BCD about CD as an axis until it coincides with A B'CD. Then, point B will fall at point... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...given line, and include an angle bisected by that line. Proposition 2O. Theorem. 30. Two triangles are equal when the three sides of one are equal respectively to the three sides of the other. Hypothesis. In the A ABC and DEF, AB = DE, AC = DF, and BC = EF. Conclusion. A ABC = A DEF. Proof.... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...equal to AB ? which side is equal to BC? RECTILINEAR FIGURES. 27 PROP. XVII. THEOREM. 69. Two triangles are equal when the three sides of one are equal respectively to the three sides of the other. D E Given, in A ABC and DEF, AB = DE, BC = EF, and CA = FD. To Prove A ABC = A DEF. Proof. Place &DEF... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1901 - 168 pages
...included angle of one are equal, respectively, to two sides and the included angle of the other. (3) lf the three sides of one are equal, respectively, to the three sides of the other. (4) If the triangles are right triangles and have a leg and the hypotenuse of one equal, respectively,... | |
 | Universities and colleges - 1917 - 140 pages
...geometry. GROUP A (Answer four questions from this group.) 1. Prove: Two triangles are congruent if the three sides of one are equal, respectively, to the three sides of the other. 2. a) Prove: If two chords intersect within a circle, the product of the segments of one is equal to... | |
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... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if... 
