 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...Proposition XIV. A Problem. 224. To divide a line harmonically. Proposition XV. A Theorem. 225. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The right triangle is divided into two triangles similar to itself and to each other.... | |
 | William Chauvenet - 1893 - 340 pages
...same number of triangles, similar each to each and similarly placed. PROPOSITION VIII. PROPOSITION IX. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle : 1st. The two triangles thus formed are similar to each othei and to... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...AO equal to В A . Connect О and C. Prove that О С is perpendicular to В С. (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 B* M c mutually... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...substitute BD for CE 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...substitute BD for CE 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... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...of two similar polygons have the same ratio as any two homologous sides. 334. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The perpendicular is a mean proportional between the segments of the hypotenuse. II.... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...Intersect, their common chord produced bisects their common tangents. 218. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the hypotenuse, and circles inscribed in the two triangles formed, their radii are proportional to the... | |
 | 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 to the whole... | |
 | 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 to the whole... | |
 | 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... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
