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
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC < BC, or EF< BC. THEOREM. 43. **Two triangles are equal, when the three sides of the one are equal** to the three sides of the other, each to each. Demonstration. Let the side AB = DE (Jig. 23), AC =... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...these results contradict the hypothesis; therefore, BAC is greater than EDF. PROPOSITION XI. 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 AB (see the diagram of Prop. 6.) be... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC < BC, or EF<BC. , . THEOREM. / / 43. **Two triangles are equal, when the three sides of the one are equal** to the three sides of the other, each to each. Demonstration. Let the side AB = DE (Jig, 23,) AC -... | |
| Adrien Marie Legendre - Geometry - 1825 - 280 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC < BC, or EF<BC. THEOREM. 43. 7\ťo **triangles are equal, when the three sides of the one are equal** to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) AC -... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...therefore, taking away the equal quantities, AG, AB, we shall have GC <[ BC, or EF<BC. THEOREM. 43. 7V0o **triangles are equal, when the three sides of the one are '< equal** to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23,) JtC =... | |
| Charles Reiner - Geometry - 1837 - 246 pages
...bdc, you will be able to find out another instance of the equality of triangles. What is it ? P. — **Two triangles are equal when the three sides of the one are equal** to the three sides of the other, each to each. M. — Right; and what angles are equal in two such... | |
| Charles Reiner - Geometry - 1837 - 254 pages
...bdc, you will be able to find out another instance of the equality of triangles. What is it ? P.—Two **triangles are equal when the three sides of the one are equal** to the three sides of the other, each to each. M.—Right; and what angles are equal in two such triangles... | |
| Adrien Marie Legendre - Geometry - 1841 - 235 pages
...BC(4l); therefore, taking away the equal quantities, AG, AB, we shall have GC<^BC, or EF<BC. THEOREM. 43. **Two triangles are equal, when the three sides of the one are equal** to the three sides of the other, each to each. Demonstration. Let the side AB = DE (fig. 23),AC = DF,... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 292 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... | |
| Eli Todd Tappan - Geometry - 1868 - 432 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... | |
| |