 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
 | George Bruce Halsted - Geometry - 1886 - 394 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.... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...angle of an isosceles triangle bisects the base, and is perpendicular to the base. PROPOSITION IX. Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. PROPOSITION X. Two right triangles are equal when... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...equal BD. PLANE GEOMETRY. — BOOK I. PROPOSITION XXXIII. THEOREM. 160. 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 = A'B', AC = A'C', BC=B'C'. To prove A ABC= A A'B'C'. Proof.... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...and homologoiis acute angle of the other. Proposition 23. Theorem. 108. Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. Htjp. Lot ABC, DEF be two As having AB = DE, AC = DF, BC = EF. To prove A ABC = A DEF. Proof. Apply... | |
 | William C. Bartol - Geometry, Solid - 1893 - 112 pages
...adjacent angles of the one are respectively equal to a side and two adjacent angles of the other. 357. Two triangles are equal when the three sides of the...equal respectively to the three sides of the other. 358. If two sides of a triangle be equal respectively to two sides of another, but the third side of... | |
 | William Chauvenet - 1893 - 340 pages
...angle of an isosceles triangle bisects the base, and is perpendicular to the base. PROPOSITION IX. Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. PROPOSITION X. Two right triangles are equal when... | |
 | Michigan Schoolmasters' Club - Education - 1894 - 554 pages
...the steps of the analysis and give the regular synthetic proof. — 31 — 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 the texts generally give before this one is taken... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...lines, then the alternate angles are equal. State and prove the converse. 2. Two triangles are equal if the three sides of the one are equal respectively to the three' sides of the other. 3. Equal chords in a circle are equidistant from the centre; and conversely. 4. The bisector of an... | |
 | Adelia Roberts Hornbrook - Geometry - 1895 - 222 pages
...one upon another, and show that they may be made to coincide in all their parts. PRINCIPLE 23. — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other. 115. AB and BD are each 7 inches, BE and BC each... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...opposite are unequal, and the greater side is opposite the greater angle. 160. Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. 161. Two right triangles are equal if a side and the hypotenuse of the one are equal respectively to... | |
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