 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...homologous. Thus, DE is homologous with AB, DF with AC, and EF with EC. THEOREM XVII. 210. In a rigjit-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotJienuse, the triangle will be divided into two triangles similar to the given triangle and to... | |
 | Harvard University - 1876 - 554 pages
...triangles are similar when they have their sides parallel each to each, or perpendicular each to each. 4. If a perpendicular is drawn from the vertex of the right angle to the hypothenuse of a right triangle : — (1) The two triangles thus formed are similar to each other and to the whole... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...the concave arc intercepted between its sides, minus half the convex arc. 2. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the hypothenuse, what relations exist between the three triangles thus formed ? Prove. How is this proposition useful... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...similar triangles And since ABC and BCD are similar AC : CB= CB: CD that is, if in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypothenuse, either side about the right angle is a mean proportional between the whole hypotenuse and the adjacent... | |
 | George Anthony Hill - Geometry - 1880 - 348 pages
...AD. therefore AB : BC = BC : BD. therefore AD : CD = CD : BD. Theorems. — If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : — I. Either leg is a mean proportional beeween the hypotenuse and the adjacent segment.... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...perimeters of two similar polygons are to each other as any two homologous lines. THEOREM XXIII. 282. If a perpendicular is drawn from the vertex of the right angle of a right-angled triangle to the hypothenuse: I. The two triangles formed are similar to the given... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...divided into equal parts, at I, K, and L PROPOSITION XXIII. THEOREM. //, in a right-angled triangle, a perpendicular is drawn from the vertex of the right angle to the Injpothenuse : 1°. Tl1e triangles on each side of the perpendicular are similar to the given triangle,... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...B'C' + C'D' + etc. A'B' B'C' C'D'' That fc P AB _BC _ CD PROPOSITION XXVII. THEOREM. 286. In any right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The triangles formed are similar to the whole triangle, and to each other. II. The... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...For we have (see preceding figures) whence (12) _ BC CD ^ B'C' C'D' '' PROPOSITION IX.—THEOREM. 25. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle: 1st. The two triangles thus formed are similar to each other and to... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...consequent). NUMERICAL PROPERTIES OF FIGURES. ^ * PROPOSITION XV. THEOREM. y 334. // in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse: I. The perpendicular is a- mean proportional between the segments of the hypotenuse. II.... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
