 In a right triangle, the perpendicular from the vertex of the right angle to the hypotenuse is a mean proportional between the segments of the hypotenuse: p2 = mn. Any two similar figures, in the plane or in space, can be placed in " perspective," that...  First Course in Algebra - Page 264by William Benjamin Fite - 1913 - 334 pagesFull view - About this book
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...equiangular with ABC, and hence similar. 72 PERPENDICULAR ON HYPOTENUSE. [BOOK V. PROP. XVIII. THEOREM. The perpendicular from the vertex of the right angle to the hypotenuse of a right-angled triangle, divides it into two triangles similar to each other, and similar to the... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...AHB be a triangle right angled at H; a, h, b, the sides respectively opposite the angles, A, H, B; p, the perpendicular from the vertex of the right angle to the hypotenuse ; m and n, segments of the hypotenuse respectively adjacent to a and b. 1. The triangle BDH is similar... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...triangle ADC? EXERCISES. 1. In a right triangle, the sides about the right angle are 12 and 15; required the length of the perpendicular from the vertex of the right angle to the hypotenuse. Suggestion. —Find the hypotenuse and one of the segments. 2. A lot is in the form of a right triangle,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...segment adjacent to that side. For from step 3, AB : AC = AC : AD ; and from 4, AB : BC = BC : DB. 2. The perpendicular from the vertex of the right angle to the hypotenuse is the mean proportional between the segments of the hypotenuse. For from step 5, AD : CD = CD : DB.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...segment adjacent to that side. For from step 3, AB : AC - AC : AD ; and from 4, AB : BC = BC : DB. 2. The perpendicular from the vertex of the right angle to the hypotenuse is the mean proportional between the segments of the hypotenuse. For from step 5, AD : CD = CD : DB.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...Given the two perpendicular sides of a right triangle equal to 8 and 6 in. respectively to compute the length of the perpendicular from the vertex of the right angle to the hypotenuse. (7.) If in a right triangle the two perpendicular sides are a and b, compute the altitude upon the... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Given the two perpendicular sides of a right triangle equal to 8 and 6 in. respectively to compute the length of the perpendicular from the vertex of the right angle to the hypotenuse. (7.) If in a right triangle the two perpendicular sides are a and b, compute the altitude upon the... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...rhombus if its diagonals are in the ratio of 4 to 7, and their sum is 16. (3.) In a right triangle the perpendicular from the vertex of the right angle to the hypotenuse divides the hypotenuse into the segments m and n. Find the area of the triangle. (4.) If the hypotenuse... | |
 | Henry W. Keigwin - Geometry - 1897 - 254 pages
...homologous medians, (2) the inradii, (3) the circumradii are in the ratio of similitude. 245. THEOREM. The perpendicular from the vertex of the right angle to the hypotenuse of a right triangle forms two similar triangles, each of which is similar to the given triangle. 246.... | |
 | Webster Wells - Geometry - 1898 - 284 pages
...joining the middle points of the parallel sides, if produced, meet in a common point. (Ex. 67.) 69. BD is the perpendicular from the vertex of the right angle to the hypotenuse of right triangle ABC. If E is any point in AB, and EF be drawn perpendicular to AC, and FG perpendicular... | |
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