| 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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