 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...and prove the triangles ABD and ACF similar. PROPOSITION XIV. THEOREM 311. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The triangles on each side of the perpendicular are similar to the -whole triangle and to each... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...and prove the triangles ABD and ACF similar. PROPOSITION XIV. THEOREM 311. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The triangles on each side of the perpendicular are similar to the whole triangle and to each... | |
 | George Albert Wentworth - 1898 - 112 pages
...perpendicular. 70. A field has the shape of a right triangle, and the two legs are 100m and 200m respectively. A perpendicular is drawn from the vertex of the right angle to the hypotenuse. How many ars are there in each part ? 7 1 . The chord of an arc is 80cm and the chord of half the arc... | |
 | Mathematics - 1898 - 228 pages
...1887. (The candidate may omit any two propositions.) 1. To inscribe a circle in a given triangle. 2. If a perpendicular is drawn from the vertex of the right angle to the hypothenuse of a right triangle: (1st.) The two triangles thus formed are similar to each other, and... | |
 | Yale University - 1898 - 212 pages
...1887. (The candidate may omit any two propositions.) 1. To inscribe a circle in a given triangle. 2. If a perpendicular is drawn from the vertex of the right angle to the hypothenuse of a right triangle: (ist.) The two triangles thus formed are similar to each other, and... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...compare with the ratio of the perpendicular to the shorter segment ? MILNE'S GEOM. — 11 Theorem. 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. Data: Any right triangle,... | |
 | William James Milne - Geometry - 1899 - 326 pages
...straight line ; that is, CD passes through A. 2. Ax. 14, CO = OB, and DP=PB; .: § 159, CD II OP. Ex. 94. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse, and circles are inscribed in the triangles thus formed, the diameters are proportional to the sides... | |
 | William James Milne - Geometry - 1899 - 398 pages
...of intersection ; and (2) that this line is parallel to the line of centers of the circles. Ex. 94. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse, and circles are inscribed in the triangles thus formed, the diameters are proportional to the sides... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...similar. BOOK III. PLANE GEOMETRY. 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... | |
 | Harvard University - Geometry - 1899 - 39 pages
...perimeters of two similar polygons are in the same ratio as any two corresponding sides. THEOREM VIII. If in a right 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 whole triangle. II. The perpendicular... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
