 | 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...: I. The two triangles thus formed are similar to eacli other and to the given triangle. II. The perpendicular is a mean proportional between the segments... | |
 | George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...sides proportional. Therefore the polygons are similar, by § 282. QED PROPOSITION XX. THEOREM 294. 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. 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.... | |
 | 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... | |
 | 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.... | |
 | 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... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...two ways : The perimeters of two similar polygons have the same ratio as any two corresponding 11. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse, state three geometric truths that follow. 12. If two secants intersect outside, on, or within a circle,... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...equals an angle of the other and the including sides are proportional. 161. Theorem VIII. If, in any right triangle, a perpendicular is drawn from the vertex of the right angle to the hypotenuse, the two right triangles thus formed are similar to each other and to the given triangle. 162. Corollary... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...2 is the mean proportional between 1 and 4, since we have 1/2 = 2/4. 161. Theorem VIII. If, in any right triangle, a perpendicular is drawn from the vertex of the right angle to the hypotenuse, the two right triangles thus formed are similar to each other and to the given triangle. Given the... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
