| William Frothingham Bradbury - Geometry - 1873 - 132 pages
...BD are 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... | |
| 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... | |
| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...triangles are equiangular to one another, (I. Ax. 1.) and the three triangles similar. . QED Cor. — Hence **the perpendicular is a mean proportional between the segments of the hypotenuse,** and each side a mean proportional between the hypotenuse and its segment adjacent to each side. For... | |
| Harvard University - 1876 - 554 pages
...for its 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... | |
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...triangle is a mean proportional between the hypotenuse and the adjacent segment of the hypotenuse ; and **the perpendicular is a mean proportional between the segments of the hypotenuse.** THEOR. 8. If from any angle of a triangle a straight line is drawn perpendicular to the base, the diameter... | |
| Robert Fowler Leighton - 1877 - 372 pages
...for its 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
...triangle into two right triangles which, are similar to the whole triangle, and also to each other. II. **The perpendicular is a mean proportional between the segments of the hypotenuse.** III. Each side of the right triangle is a mean proportional between the hypotenuse and its adjacent... | |
| 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... | |
| George Anthony Hill - Geometry - 1880 - 332 pages
...'54£\ABC~ABCD; therefore AB : BC = BC: BD. AA CD ~ ABCD ; therefore AD : CD. = CD : BD. Theorems. — If **in a right triangle a perpendicular is drawn from...vertex of the right angle to the hypotenuse : — I.** Either leg is a mean proportional beewecn the hypotenuse and the adjacent segment. II. The perpendicular... | |
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