If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent. Elements of Geometry - Page 9by Adrien Marie Legendre - 1841 - 235 pagesFull view - About this book
| Benjamin Donne - 1796
...the line DF will coincide with AC, and EF with BC. THEOREM 16. If two triangles have three sides of **one equal to the three sides of the other, each to each,** thefe triangles are equal in every rcfpeft. — 8 E. 1, or 17 D. 1. Ciť For if the triangle DEF be... | |
| Daniel Cresswell - Geometry - 1816 - 294 pages
...which are equal to them, are equal to one another. (2l6.) COR. 2. Hence, if two spherical triangles **have the three sides of the one equal to the three sides of the other,** or two sides and the included angle in the one, equal to two sides and the included angle, in the other,... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...FG ; but, by hypothesis, BC : EF : : AC : DF ; consequently FG = DF ; hence the triangles EGF, DEF, **have the three sides of the one equal to the three sides of the other, each to each** ; they are therefore equal (43). But, by construction, the triangle EGF is equiangular with the triangle... | |
| Adrien Marie Legendre - 1825 - 224 pages
...angles opposite to the equal sides are equal. Demonstration. Let the side AB = AC (fig. 28), then will **the angle C be equal to B. Draw the straight line...also equiangular, that is, it has its angles equal.** 47. Scholium. From the equality of the triangles ABD, ACD, it follows, that the angle BAD— DAC, and... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...to the equal sides are equal. Demonstration. Let the side AB = AC (fig. 28), then will the Fig.;28. **angle C be equal to B. Draw the straight line AD from...sides of the one, equal to the three sides of the** qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...the figure will be a parallelogram. Demonstration. Draw the diagonal BD ; the two triangles ABD, BDC, **have the three sides of the one equal to the three sides of the other, each to each,** they are therefore equal, and the angle ADB opposite to the side AB is equal to the angle DBC opposite... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. having **the three sides of the one equal to the three sides of the other, each to each,** are also equal. 162. Two figures are similar, which have the angles of the one equal to the angles... | |
| George Lees - 1826
...base at right angles. OF GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, **have the three sides of the one equal to the three sides of the other, each to each,** viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let AB be that side... | |
| James Hayward - Geometry - 1829 - 172 pages
...their parts ; they are not different, therefore, but equal; and we say, universally, When two triangles **have the three' sides of the one equal to the three sides of the other** respectively, the angles will also be equal, respectively, and the two triangles will be equal in all... | |
| Alexander Ingram - Mathematics - 1830 - 120 pages
...one and the same great circle, meet in the poles of that circle. PROP. V. If two spherical triangles **have the three sides of the one equal to the three sides of the other, each to each,** the angles which are opposite to the equal sides are likewise equal ; and conversely. PROP. VI. If... | |
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