 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...equal parts at F and G, 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
...of the opposite side is 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
...of the opposite side is 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 ef the right angle to the opposite side, .the two triangles so formed are equiangular with each other... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...they are composed of 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... | |
 | United States. War Department - 1903 - 446 pages
...straight line, to describe a segment of a circle in which a given angle may be inscribed. 3. Theorem. — If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse. (a) The triangles thus formed are similar to the given triangle and to each other. (b) The perpendicular... | |
 | United States. War Department - 1903 - 438 pages
...straight line, to describe a segment of a circle in which a given angle may be inscribed. 8. Theorem. — If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse. (a) The triangles thus formed are similar to the given triangle and to each other. (6) The perpendicular... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...similar triangles, AC _ AB AB ~ AD And since ABC and BCD are similar, AC __ CB C~B ~= C~D' that is, if in a right triangle, a perpendicular is drawn from the vertex of the right angle to the hypothenuxe, either side about the right angle is a mean proportional between the wliole hypothenuse,... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...173. Problem XVI. To divide a given line into parts proportional to any given lines. THEOREM XII 174. If in a right triangle a perpendicular is drawn from the vertex of tJie right angle to the hypotenuse : I. The triangles thus formed are similar to the whole triangle.... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...equal vertical angles are similar. NUMERICAL PROPERTIES OF FIGURES. PROPOSITION XXVII. THEOREM. 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... | |
 | Yale University. Sheffield Scientific School - 1905 - 1074 pages
...unequal, the opposite sides are also unequal, and thegreater side is opposite the greater angle. 2. In a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse. State and prove three theorems true of the figure thus formed. 3. The bisector of an angle (interior... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
