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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

## An Elementary Geometry

William Frothingham Bradbury - Geometry - 1873 - 132 pages
...BD are similar triangles AC :AB = AB:AD 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 hypothenuse...

## New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...is homologous with AB, DF with AC, and EF with BC. THEOREM XVII. 210i In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle and to each...

## New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...homologous with AB, DF with AC, and EF with £ C. THEOREM XVII. 210. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle and to each...

## Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...triangles are equiangular to one another, (I. Ax. 1.) and the three triangles similar. . QED Cor. — Hence the perpendicular is a mean proportional between the segments of the hypotenuse, and each side a mean proportional between the hypotenuse and its segment adjacent to each side. For...

## Catalogue - Harvard University

Harvard University - 1876 - 554 pages
...for its measure half 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...

## Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

...triangle is a mean proportional between the hypotenuse and the adjacent segment of the hypotenuse ; and the perpendicular is a mean proportional between the segments of the hypotenuse. THEOR. 8. If from any angle of a triangle a straight line is drawn perpendicular to the base, the diameter...

## Harvard Examination Papers

Robert Fowler Leighton - 1877 - 372 pages
...for its measure half 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...

## Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...triangle into two right triangles which, are similar to the whole triangle, and also to each other. II. The perpendicular is a mean proportional between the segments of the hypotenuse. III. Each side of the right triangle is a mean proportional between the hypotenuse and its adjacent...