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" The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude. "
Plane Geometry - Page 71
by George Albert Wentworth - 1899 - 256 pages
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Selected Propositions in Geometrical Constructions and Applications of ...

Adrien Marie Legendre - Geometry - 1882 - 194 pages
...construct on it a square, as before. fi. — Show that the sum of the. three perpendiculars, drawn from any point within an equilateral triangle to the three sides, is equal U the altitude of the triangle. Let ABC be an equilateral triangle, and BD its altitude. From...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...respectively 16, 12, 8, 4, and 2 units in length. 5. Show that the sum of the three perpendiculars drawn from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. 6. Show that the sum of the squares of two lines, drawn from...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...the two Js, BF the altitude upon AC. Draw PG to BF, and prove the A PSG and PBD equal. . . P 74. The sum of the perpendiculars dropped from any point...three sides is constant, and equal to the altitude. HINT. Draw through the point a line II to the base, and apply Ex. 73. 75. What is the locus of all...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...from any point in the base is constant (see Ex. 133). Show also that the sum of the perpendiculars from any point within an equilateral triangle to the three sides is constant. Ex. 681.— ABC, DBC are two triangles on the same base BC : the line joining the vertices A and D...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...difference of its distances from the equal sides is constant. 24. The sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is equal to the perpendicular drawn from any one of the angular points to the opposite side, and is therefore...
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Exercises in Wentworth's Geometry: With Solutions

George Albert Wentworth - Geometry - 1896 - 296 pages
...is common. .-. A PBD = A PEG. .: PD = BG. PE= GF. .: PD + PE= BG + GF= BF. (g 148) (g 180) Ex. 74. The sum of the perpendiculars dropped from any point...three sides is constant, and equal to the altitude. Let ABC be an equilateral A, BC the base, AD the altitude, P any point within the A, PE, PF, PG _!•...
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Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 214 pages
...triangles have the same ratio as any two homologous sides. Prove. 5. The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. Prove. Boston University, September, 1896. TIME 1 H. 80 M. [Candidates...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...parallelogram divides the parallelogram into two equivalent figures. 294. The sum of the perpendiculars drawn from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. 295. The area of a triangle is equal to the product of the semiperimeter...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 264 pages
...(Ex. 13, p. 173.) (Represent the diagonals by 2 a; and 2 y.) A j 43. The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle. "/-'' DE 44. The longest sides of two similar polygons are 18...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 498 pages
...(Why ?) .-. GF = PE. It remains to prove GB = PD. The rt. A PGB = the rt. A BDP. (Why ?) A — J- "B Ex. 61. The sum of the perpendiculars dropped from...Then MD = PE. (Why ?) PG + PF = AM (Ex. 60). Ex. 62. ABC and ABD are two triangles on the same base AB, and on the same side of it, the vertex of each triangle...
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