 | William James Milne - Geometry, Modern - 1899 - 258 pages
...of the perpendicular to the shorter segment ? MILNE'S GEOM. — 11 Theorem. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse, the perpendicular is a mean proportional between the segments of the hypotenuse. Data: Any right triangle,... | |
 | William James Milne - Geometry - 1899 - 326 pages
...passes through A. 2. Ax. 14, CO = OB, and DP=PB; .: § 159, CD II OP. Ex. 94. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse, and circles are inscribed in the triangles thus formed, the diameters are proportional to the sides... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...the same number of triangles, similar each to each, and similarly placed. 367. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : 1. The triangles thus formed are similar to the given triangle, and to each other. 2. The perpendicular... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...GEOMETRY PROPOSITION XXI. THEOREM 518. In a right-angled triangle, if a perpendicular is drawn from tlie vertex of the right angle to the hypotenuse, I. The...each side of the perpendicular are similar to the original triangle, and to each other. II. The perpendicular is a mean proportional between the segments... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...PROPOSITION XXI. THEOREM 518. In a right-angled triangle, if a perpendicular is drawn from the vertex of tJte right angle to the hypotenuse, I. The triangles on each side of the perpendicular are similar to the original triangle, and to each other. II. The perpendicular is a mean proportional between the segments... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...then DE is divided into equal parts at H and I. PROPOSITION XXV. — THEOREM. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse, 1st. The triangles on each side of the perpendicular are similar to the given triangle and to each... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...equal to half of this side, prove that the triangle has one right angle. 3. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the opposite side, the two triangles so formed are equiangular with each other and with the whole triangle.... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...polygons are in the same ratio as any two corresponding sides. § 254. (5) If in a right triangle the perpendicular is drawn from the vertex of the right angle to the hypotenuse: (1) the two triangles thus formed are similar to each other and to the whole triangle ; (2) the perpendicular... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...the same number of triangles, similar each to each, and similarly placed. 367. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse: 1. The triangles thus formed are similar to the given triangle, and to each other. 2. The perpendicular... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...BZ = BC_. (j) l' *• ; XB AB' ZA AC' TC Whence AY PROPOSITION XXI. THEOREM 518. In a right-angled triangle, if a perpendicular is drawn from the vertex...each side of the perpendicular are similar to the original triangle, and to each other. II. The perpendicular is a mean proportional between the segments... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
