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" If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4. "
The Essentials of Geometry (plane) - Page 151
by Webster Wells - 1898 - 242 pages
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...equiangular with ABC, and hence similar. 72 PERPENDICULAR ON HYPOTENUSE. [BOOK V. PROP. XVIII. THEOREM. The perpendicular from the vertex of the right angle to the hypotenuse of a right-angled triangle, divides it into two triangles similar to each other, and similar to the...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...AHB be a triangle right angled at H; a, h, b, the sides respectively opposite the angles, A, H, B; p, the perpendicular from the vertex of the right angle to the hypotenuse ; m and n, segments of the hypotenuse respectively adjacent to a and b. 1. The triangle BDH is similar...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...EXERCISES. 1. In a right triangle, the sides about the right angle are 12 and 15; required the length of the perpendicular from the vertex of the right angle to the hypotenuse. Suggestion. —Find the hypotenuse and one of the segments. 2. A lot is in the form of a right triangle,...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...intersect each other, their common chord produced bisects their common tangents. ( 293.) 3. If one side of a, right triangle is 'double the other, the perpendicular...it into segments which are to each other as 1 to 4. 4. If two parallels to the side BC of a triangle meet the sides AB and AC in the points D and F, and...
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Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...extremity of the bisector extended, then the triangles BAD and ACE can be proved similar. 375. If one side of a right triangle is double the other, the perpendicular, from the vertex of the right angle to the hypothenuse, divides it into segments which are to each other as 1 to 4. 376. A line parallel to the...
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Manual of Plane Geometry: On the Heuristic Plan, with Numerous Extra ...

George Irving Hopkins - 1891 - 210 pages
...triangle is double the other, the perpendicular, from the vertex of the right angle to the hypothenuse, divides it into segments which are to each other as 1 to 4. 376. A line parallel to the bases of a trapezoid, passing through the intersection of the diagonals,...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...intersecting circles is 16, and their radii are 10 and 17, what is the distance between cheir centres ? 22. If one leg of a right triangle is double the other,...it into segments which are to each other as 1 to 4. 23. If two parallels to the side BC of a triangle ABC meet the sides AB and AC in D and F, and E and...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...10 and 17, what is the distance between cheir centres ? 22. If one leg of a right triangle is douhle the other, the perpendicular from the vertex of the...it into segments which are to each other as 1 to 4. 23. If two parallels to the side BC of a triangle ABC meet the sides AB and AC in D and F, and E and...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...segment adjacent to that side. For from step 3, AB : AC - AC : AD ; and from 4, AB : BC = BC : DB. 2. The perpendicular from the vertex of the right angle to the hypotenuse is the mean proportional between the segments of the hypotenuse. For from step 5, AD : CD = CD : DB....
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...segment adjacent to that side. For from step 3, AB : AC = AC : AD ; and from 4, AB : BC = BC : DB. 2. The perpendicular from the vertex of the right angle to the hypotenuse is the mean proportional between the segments of the hypotenuse. For from step 5, AD : CD = CD : DB....
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