 | 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...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 or exterior)... | |
 | Cora Lenore Williams - Geometry - 1905 - 56 pages
...116. Polygons similar to the same polygon are similar to each other. Prop. 117. If in a right-angled triangle, a perpendicular is drawn from the vertex of the right angle to the hypotemuse, it divides the triangle into two right triangles which are similar to the whole triangle,... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...two similar polygons are in the same ratio as any two corresponding sides. 359. If in a right-angled triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The two triangles thus formed are similar to eacli other and to the given triangle. II. The perpendicular... | |
 | Geometry, Plane - 1911 - 192 pages
...the bisector of the second. When are the two bisectors parallel? When perpendicular? 2. Prove that 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. Prove that if the... | |
 | David Eugene Smith - Geometry - 1911 - 370 pages
...pupil in geometry can measure most of the heights and distances in which he is interested. THEOREM. 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 are similar to each other. 2.... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...of the angle, an angle is formed which is equal to the given angle. Ex. 219. In a right triangle if a perpendicular is drawn from the vertex of the right angle to the hypotenuse, the right angle is divided into two angles which are equal respectively to the acute angles of the... | |
 | Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...being homologous to a'. 2. Then use § 190. (The proof is left to the pupil.) THEOKEM XLVI 192. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle, I. The triangles formed are similar to the whole triangle, and to each other.... | |
| |
If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
