 If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is a right triangle.  Plane Trigonometry - Page 74by Arnold Dresden - 1921 - 110 pagesFull view - About this book
 | Euclides - 1840 - 82 pages
...angle, is equal to the squares of the sides which contain the right angle. r E PROP. XLVIII. THEOR. If the square of one side of a triangle is equal to the squares of the other two sides, the angle subtended by that side is a right angle. BOOK II. PROP. I.... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...subtraction. Also, the sine bf either angle is equal to the sine of the sum of the other two. 305 Theorem — The square of one side of a triangle is equal to the sum of the squares of the other two sides, less twice the product of those sides by the cosine of their included... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...AC2-f-CB2 -(- 2CB.CD when Z ACB is obtuse. CoR. It is evident that 2CB.CD = 0 only when Z ACB=R : hence, if the square of one side of a triangle is equal to the sum of the squares of the other two sides, the angle between these sides is a right angle (converse of 12).... | |
 | Samuel Biggar Giffen McKinney - Christianity - 1888 - 556 pages
...by making the drawing necessary to prove the forty-seventh proposition of the first book of Euclid. The square of one side of a triangle is equal to the sum of the squares of the other two sides only if the triangle contains a right angle. There will be perfect... | |
 | Edwin Pliny Seaver - Trigonometry - 1889 - 306 pages
...and [119Z>] can easily be proved geometrically from Figure 61. This is proposed as an exercise. 182. The square of one side of a triangle is equal to the sum of the squares of the other two sides less twice the product of these sides multiplied by the cosine of... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...rectangle of the hypotenuse and the projection of the given side upon the hypotenuse. Corollary III. If the square of one side of a triangle is equal to the sum of the squares of the two other sides, the triangle is a right-angled triangle. PROPOSITION XXV. 219.... | |
 | Henry Sinclair Hall, Samuel Ratcliffe Knight - Plane trigonometry - 1893 - 434 pages
...negative ; that is, the projection of OP = projection of OQ + projection of QP, Hence, the projection of one side of a triangle is equal to the sum of the projections of the other two sides taken in order. Thus projection of 0§=projection of OP+projection... | |
 | Edwin Bidwell Wilson, Josiah Willard Gibbs - Vector analysis - 1901 - 476 pages
...OB of a triangle OAB, the third o~ side A£isC = BA. (Fig. 17). BC FIG. 17. 1 + AA-2A-B or That is, the square of one side of a triangle is equal to the sum of the squares of the other two sides diminished by twice their product times the cosine of the angle... | |
 | Arthur Schultze - 1901 - 260 pages
...the squares of two opposite sides is equal to the sum of the squares of the other two. Ex. 628. If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is a right triangle. * Ex. 629. If the square of one... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...the squares of two opposite sides is equal to the sum of the squares of the other two. Ex. 628. If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is a right triangle. * Ex. 629. If the square of one... | |
| |
