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" If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. "
Elements of Geometry: Plane geometry - Page 140
by Andrew Wheeler Phillips, Irving Fisher - 1896
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Catalogue - Harvard University

Harvard University - 1876 - 554 pages
...triangles are similar when they have their sides parallel each to each, or perpendicular each to each. 4. If a perpendicular is drawn from the vertex of the right angle to the hypothenuse of a right triangle : — (1) The two triangles thus formed are similar to each other and...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...a right-angled triangle, if a perpendicular is drawn from the right angle to the hypothenuse ; 1st. The triangles on each side of the perpendicular are similar to the whole triangle and to each other. 2d. The perpendicular is a mean proportional between the segments of the hypothenuse. 3d. Each of the...
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 372 pages
...the concave arc intercepted between its sides, minus half the convex arc. 2. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the hypothenuse, what relations exist between the three triangles thus formed ? Prove. How is this proposition...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...similar A are proportional). QED PROPOSITION X. THEOREM. 289. If in a right triangle a perpendicular be drawn from the vertex of the right angle to the hypotenuse : I. It divides the triangle into two right triangles which, are similar to the whole triangle, and also...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 100 pages
...8). In a right angled triangle if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of the perpendicular are similar to the whole triangle, and to ene another. And if the right-angled triangle have its two sides equal, any triangles made within it...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 348 pages
...AD. therefore AB : BC = BC : BD. therefore AD : CD = CD : BD. Theorems. — If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : — I. Either leg is a mean proportional beeween the hypotenuse and the adjacent segment. II. The perpendicular...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...similar triangles And since ABC and BCD are similar AC : CB= CB: CD that is, if in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypothenuse, either side about the right angle is a mean proportional between the whole hypotenuse...
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Elements of Geometry

George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...pass through a common point. PROPOSITION X. THEOREM. 289. If in à right triangle a perpendicular be drawn from the vertex of the right angle to the hypotenuse : I. It divides the triangle into two right triangles which are similar to the whole triangle, and also...
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Elements of Plane Geometry

Franklin Ibach - Geometry - 1882 - 208 pages
...perimeters of two similar polygons are to each other as any two homologous lines. THEOREM XXIII. 282. If a perpendicular is drawn from the vertex of the right angle of a right-angled triangle to the hypothenuse: I. The two triangles formed are similar to the given...
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A Geometry for Beginners

George Anthony Hill - 1884 - 350 pages
...therefore AB : BC = BC: B D. t\ACD~t\BCD; therefore AD: CD = CD: BD. Theorems. — If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse: — Fig. 154. I. Either leg is a mean proportional beeween the hypotenuse and the adjacent segment....
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