 ... lines, and the perpendiculars from the three vertices of the triangle upon this line will be equal, by Chap. I, II, 13. A perpendicular to AB erected midway between any two of these three is perpendicular to the corresponding side of the triangle...  Elements of Analytic Geometry - Page 57by Joseph Johnston Hardy - 1897 - 365 pagesFull view - About this book
 | Edward Albert Bowser - Geometry, Analytic - 1880 - 334 pages
...axes may be oblique or rectangular, the result being the same. EXAMPLES. 1. Find the co-ordinates of the middle points of the sides of the triangle whose vertices are (2, 3), (4, —5), (— 3, —6). Ans. (i, -J¿), (-t, -t), (3, -1). 2. The line joining the points... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...EM passes through 0; . ' . DH, FG, and EM meet in a common point. QED 106. COR. — The common point of the perpendiculars erected at the middle points of the sides of a triangle is equally distant from the vertices of the triangle. POLYGONS. DEFINITIONS. 107. A Polygon... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...erected at the middle points of the sides of a triangle meet in a common point. Let DG, EH, and FK be the perpendiculars erected at the middle points of the sides of the triangle ABC. To prove that they meet in a common point. Let DG and EH intersect at 0. Then since 0 is in the... | |
 | George Albert Wentworth - Geometry, Analytic - 1886 - 346 pages
...that these perpendiculars meet in one point. 33. The equations of the sides of a triangle are Find (i) the equations of the perpendiculars erected at the middle points of the sides ; (ii) the coordinates of their common point of intersection ; (iii) the distance of this point from... | |
 | George Albert Wentworth - 1894 - 362 pages
...through the point (6, 2), and is parallel to the axis of y. Whence its equation is x = 6. 32. Find the equations of the perpendiculars erected at the...(— 4, 13). Prove that these perpendiculars meet in one point. From [2], the mid-point between (5, — 7) and (1, 11) is (3, 2). From [4], the line through... | |
 | John Henry Tanner, Joseph Allen - Geometry, Analytic - 1898 - 458 pages
...vertices are the points (2, 1 ), (3, -2), (-4, -1) is a right triangle. 10. Prove analytically that the perpendiculars erected at the middle points of the sides of the triangle, the equations of whose sides are x + y +1 = 0, 3x + oy+U=0, and x + 2y + 4 = 0, meet in a point which... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...also equally distant from A and C; the theorem follows by § 42.) 137. Cor. The point of intersection of the perpendiculars erected at the middle points of the sides of a triangle, is equally distant from the vertices of the triangle. EXERCISES. 48. If the diagonals of... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...also equally distant from A and C; the theorem follows by § 42.) 137. Cor. The point of intersection of the perpendiculars erected at the middle points of the sides of a triangle, is equally distant from the vertices of the triangle. EXERCISES. 48. If the diagonals of... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...also equally distant from A and C; the theorem follows by § 42.) 137. Cor. The point of intersection of the perpendiculars erected at the middle points of the sides of a triangle, is equally distant from the vertices of the triangle. EXERCISES. 48. If the diagonals of... | |
 | Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 122 pages
...perpendicular to the corresponding side of the triangle at its middle point (Chap. 1, 1, 11). Thus, all three of the perpendiculars erected at the middle points of the sides of the triangle are perpendicular to AB. A line is parallel to a plane if it is parallel to its projection on the plane.... | |
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