 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...angles are similar. NUMERICAL PROPERTIES OF FIGURES. PROPOSITION XXVII. THEOREM. 367, If in a r'ujht 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... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...CD equal to 2 units, the value of CE is V6. Proposition 149. Theorem. 183. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse, the squares of the legs are in the same ratio as the adjacent segments of the hypotenuse, and the ratio... | |
 | Webster Wells - Geometry - 1899 - 450 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. I. To... | |
 | Webster Wells - Geometry - 1899 - 424 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.... | |
 | United States Naval Academy - 1899 - 624 pages
...of a right triangle from the vertex of Hie right angle, the two triangles so formed are similar, and the perpendicular is a mean proportional between the segments of the hypotenuse. Show how to construct a mean proportional between two lines. 4. Prove that the area of a triangle is... | |
 | Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 165 pages
...the hypotenuse, then the triangles so formed are similar to each other and to the whole triangle ; the perpendicular is a mean proportional between the segments of the hypotenuse ; and each side is a mean proportional between the adjacent segment of the hypotenuse and the hypotenuse.... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...parts at F and G, then DE is divided into equal parts at H and I. PROPOSITION XXV. — THEOREM. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse, 1st. The triangles on each side of the perpendicular are similar to the given triangle and to each... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...the opposite side is equal to half of this side, prove that the triangle has one right angle. 3. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the opposite side, the two triangles so formed are equiangular with each other and with the whole triangle.... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...polygons are in the same ratio as any two corresponding sides. § 254. (5) If in a right triangle the perpendicular is drawn from the vertex of the right angle to the hypotenuse: (1) the two triangles thus formed are similar to each other and to the whole triangle ; (2) the perpendicular... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...triangles on each side of the perpendicular are similar to the original triangle, and to each other. II. The perpendicular is a mean proportional between the segments of the hypotenuse. III. Either side about the perpendicular is a mean proportional between the hypotenuse and the adjacent... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
