...of § 249, 052 = AD X BD, AC2 = ABx AD, and BC2 = AB x BD. (?) Hence, if a perpendicular be draivn from the vertex of the right angle to the hypotenuse of a right triangle, 1. The square of the perpendicular is equal to the product of the segments of the hypotenuse. 2. The...

...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...

...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...

...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....

...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 of the...

...7. 9. a = 11, b = 21. 4. a = 1, i = 6. 4. a = 7,1 = 11. 10. a = 13, 6 = 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, - = т- If o = 1.3 and 6 = 4, what is the length of p?...

...DB, we obtain AD/CD — CD/DB, which was to be proved. 163. Corollary 2. If, in any right triangle, a perpendicular is drawn from the vertex of the right angle to the hypotenuse, each side of the right triangle is the mean, proportional between the hypotenuse and the segment adjacent...

...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...

...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...

...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,...