 If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The two triangles thus formed are similar to each other and to the whole triangle. II. The perpendicular is a mean proportional between the segments...  Plane and Solid Geometry - Page 134by Elmer Adelbert Lyman - 1908 - 340 pagesFull view - About this book
 | André Darré - 1872 - 226 pages
...+ b2. But A8 = a2 + b2 (90), consequently, S = s + «i. THEOREM. 120. In a right-angled triangle if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the square or any other figure on the hypothenuse is to the square or other similar figure... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...similar triangles AC :AB = AB:AD 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 hypothenuse... | |
 | William Frothingham Bradbury - Geometry - 1873 - 288 pages
...triangles AC :AB — AB :AD 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 hypothenuse... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...is homologous with AB, DF with AC, and EF with BC. THEOREM XVII. 210i In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle and to each... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...homologous with AB, DF with AC, and EF with £ C. THEOREM XVII. 210. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle and to each... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...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 Hie whole triangle; 2d. The perpendicular is a mean proportional between the segments of the hypotenuse;... | |
 | Harvard University - 1876 - 554 pages
...measure half 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... | |
 | 1876 - 646 pages
...a perpendicular be drawn from the vertex of the right angle to the hypothenuse of a right triangle, the two triangles thus formed are similar to each other and to the whole triangle. (b) What can you say of the perpendicular as compared with the segments of the hypothenuse?... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...measure half 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... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...similar A are proportional). QED PROPOSITION X. THEOREM. 289. If in a right triangle a perpendicular be drawn from the vertex of the right angle to the hypotenuse : I. It divides the triangle into two right triangles which, are similar to the whole triangle, and also... | |
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