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" IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 92
by Dennis M'Curdy - 1846 - 138 pages
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Examinations Papers

1886
...Prove that if the points A, K, L, G be in a straight line DC is parallel to EF. •6. In a right-angled triangle, if a perpendicular be drawn from -the right angle to the base, either side is a mean proportional between ihe base and the segment of the base adjacent to that side....
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Annual Report

Canada. Department of the Interior - 1888 - 756 pages
...in a given circle. 12. Define proportion, similar figures, homologous, extreme and mean ratio. 13. In a right angled triangle, if a perpendicular be...triangles on each side of it are similar to the whole triangle and to one another. 14. On a given straight line to describe a rectilineal figure similar...
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Examinations Papers

1888
...straight line joining the points of bisection will be trisected by the sides. 6. In a right-angled triangle if a perpendicular be drawn from the right angle to the hypotenuse, the triangles on each side of it are similar to the triangle and to one another. State...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 354 pages
...and parallelograms of the same altitude are to one another as their bases. 2 10. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle, and. to one another. If AD be the perpendicular, and AB, AC the two sides including the right...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...their sides about the equal angles reciprocally proportional. 8. In a right-angled triangle, show that if a perpendicular be drawn from the right angle to...triangles on each side of it are similar to the whole triangle and to each other. ABC is a triangle ; AD is drawn perpendicular to BC, meeting it in D between...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 440 pages
...aright-angled triangle, if a perpendicular is drawn from the right angle on the hypotenuse — (a) the triangles on each side of it are similar to the whole and to each other : (j3) the perpendicular is a mean proportional between the segments of the hypotenuse : (y) each of...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...the Theorem enunciated, but incidentally the following highly important one : — In a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the square on either of the sides containing the right angle is equal to the rectangle contained by the...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...NUMERICAL BELATIONS BETWEEN THE DLFFEREXT PAETS OF A TRIANGLE. Proposition 24. Theorem. 323. In a right triangle, if a perpendicular be drawn from the right angle to the hypotenuse : (1) The two triangles on each side of it are similar to the whole triangle and to each...
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Annual Report of the Chief Superintendent of Education

1891 - 720 pages
...times the angle in the other. 4. Inscribe a regular hexagon in a given circle. 5. In a right-angled triangle, if a perpendicular be drawn from the right...triangles on each side of it are similar to the whole triangle and to one another. 6. Cut a given straight line in extreme and mean ratio. IM ALGEBRA. Time,...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...given the base, the altitude and the length of the median which bisects the base. 3. In a right-angled triangle if a perpendicular be drawn from the right angle to the hypothenuse, the two triangles thus formed are equiangular to one another. 4. Every right-angled triangle...
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