...making AO equal to B A. Connect O and C. Prove that OC is perpendicular to B C. (Ex. 112.) Ex. 119. If a perpendicular is drawn from the vertex of the right angle of a right-angled triangle to the hypotenuse, prove that the two triangles formed are BM c mutually...

...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 each other and to the given triangle....

...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...

...to the sides 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...

...respectively, a being homologous to a'. To prove = a b_ a' + b' + c' + d' + e' a' b' THEOREM 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...

...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...

...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...

...5, b = 7. 9. a = 11, b = 21. 4. a = 1, 6 = 6. 7. а = 7, 6 = 11. 10. я = 13, b = 29. 11. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse, as shown in the figure, then, as in § 165, - =|- If a = 1.3 and b = 4, what is the length...

...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...

...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....