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" If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. "
A Text-book of Geometry - Page 152
by George Albert Wentworth - 1888 - 386 pages
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 264 pages
...a right triangle, I. The triangles formed are similar to the whole triangle, and to each other. II. The perpendicular is a mean proportional between the segments of the hypotenuse. III. Either leg is a mean proportional between the whole hypotenuse and the adjacent segment. ADB I....
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...A'E'' P = AE P ' A'E' QED PROPOSITION XVII. THEOHKM. 227. 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 ichich are similar to the whole triangle, and also...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...follows that : If a perpendicular be drawn from any point in the circumference of a circle to a diameter, I. The perpendicular is a mean proportional between the segments of the diameter. 2. The chord joining the point to either extremity of the diameter is a mean proportional...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

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...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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Key to Milne's Plane and Solid Geometry

William James Milne - Geometry - 1899 - 326 pages
...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...
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Plane Geometry

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,...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...they are composed of the same number of triangles, similar each to each, and similarly placed. 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...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 396 pages
...the perpendicular compare with the ratio of the perpendicular to the shorter segment ? 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,...
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Plane Geometry

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...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 pages
...equal vertical angles are similar. NUMERICAL PROPERTIES OF FIGURES. PROPOSITION XXVII. THEOBEM. 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...
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