 | Pierce Morton - Geometry - 1830 - 584 pages
...the straight line which joins the middle point of the diagonals. . . .23 (c) I f two quadrilaterals have three sides of the one equal to three sides of the other, each to each, and the angles of the one lying in the circumference of a circle of which the fourth side is diameter,... | |
 | Mathematics - 1835 - 684 pages
...indefinite, inclose the greatest possible area, when placed at right angles. PROP. 40. If two quadrilaterals have three sides of the one equal to three sides of the other, each to each, and the angles of the first lying in a semi- circumference of which the fourth side Is diameter, but... | |
 | Charles Hutton - Mathematics - 1843 - 570 pages
...the spherical triangle ABC, are greater than two right angles. PROP. XVI. THEOREM. If two triangles have three sides of the one equal to three sides of the other, each to each ; the angles will be equal which are opposite to the equal sides : and conversely, if the three angles... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...CAB of the spherical triangle ABC arc greater than two right angles. PROPOSITION EX. If two triangles have, three sides of the one equal to three sides of the other, each to each, the angles will be equal which are opposite to the equal sides ; and conversely, if the three angles... | |
 | Euclides - 1856 - 168 pages
...circle A, and the two circles will meet each other in the points D and E only. XXXIV. If two triangles have three sides of the one equal to three sides of the other, each to each, the angles of the one shall be equal to the angles of the other each to each, namely, those to which... | |
 | University of Calcutta - 1864 - 388 pages
...rectangle is a parallelogram. Is it true that every parallelogram is a rectangle ? Give reasons for your answer. (c.) Two triangles that have three sides of...difference between the equality of the triangles in these two cases ? If so, whai ? . (dJ lu the first book of Euclid, what properties are shown to belong to... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...FD; (Ax. 2.) also AD is equal to BC, and AF to BE. (I. 24. ) Therefore the two triangles CEB, FDA, have three sides of the one equal to three sides of the other, and they are therefore equal in area. (I. 6.) From each take the common part DEO, therefore the four-sided... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...symmetrical, and equal (15). XXIV. If two spherical triangles on the same sphere, or equal spheres, have three sides of the one equal to three sides of the other, each to each, their angles will be equal each to each; and the triangles are congruent or symmetrical, and equal... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...the / -,. quadrilateral ABDC be a parallelogram. For, having drawn BC, the two triangles ABC and DCB have three sides of the one equal to three sides of the other, each to each; hence they are every way equal (Prop. VII., Bk. I.); and the angle ABC is equal to the angle BCD: these... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...cutting in C. ABC is an equilateral triangle. Proposition 4. Tlieorem.—If two triangles have the three sides of the one equal to three sides of the other, each to each, the angles of one will be equal to the angles of the other, each to each; the equal angles being opposite... | |
| |
If two triangles have three sides of the one equal to three sides of the other, each to each, the triangles are congruent. 
