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" Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point. "
Plane and Solid Geometry - Page 74
by Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 pages
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...triangles, or an isosceles triangle can be added to it so as to form with it an isosceles triangle. 186. The perpendiculars from the vertices of a triangle to the opposite sides respectively bisect the angles of the triangle formed by joining the feet of these perpendiculars....
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...triangles, or an isosceles triangle can be added to it so as to form with it an isosceles triangle. 186i The perpendiculars from the vertices of a triangle to the opposite sides respectively bisect the angles of the triangle formed by joining the feet of these perpendiculars....
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Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 222 pages
...line drawn from A to the point D must pass through 0. Hence the three lines meet in a point. PROP. 21. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point: and if a triangle be formed by joining their feet, its sides will be equally inclined...
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Texas School Journal, Volume 20

Education - 1902 - 730 pages
...— |- D But substituting a a + ar ar+ar» 1-fr 1+r 1+r 1. PLANE GEOMETRY. Answer any five. 1. Prove: The perpendiculars from the vertices of a triangle to the opposite sides meet in a common point. What is the name of this point? 2. A circle is inscribed in a triangle ABC....
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...of a triangle is equally distant from the vertices of the triangle. PROPOSITION XLIII. THEOREM. 129. The perpendiculars from the vertices of a triangle to the opposite sides meet in a common point. Let AD, BE, and CF be the perpendiculars from the vertices of the triangle...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 264 pages
...A and .5. Hence O is equidistant from B and C, and therefore is in the _L bisector FF'. (Why ?) 32. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. HINT. Let the _k be AH, BP, and Through A, B, C suppose B'C', A'C', A'B' drawn II...
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Examinations Papers

1888 - 666 pages
...the third booi 1 Is it completely treated ? Give fully -the reasons for your answer. 2. Prove that the perpendiculars from the vertices of a triangle to the opposite sides pass through a point, and that the circle which passes through . • the feet of these perpendiculars...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...great as either of the angles A and B, find the value of the angle AOB. Proposition 43. Theorem. 170. The perpendiculars from the vertices of a triangle, to the opposite sides are concurrent. Hyp. Let ABC be a A, and AD, BE, CF the three J_s from A, B, C to the opp. sides. To prove that these...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...pt., being the _L bisectors oflhe three sides oftfie A PQR (168). QED 171. DsF. The intersection of the perpendiculars from the vertices of a triangle to the opposite sides is called its arthocentrc, --" Proposition 44. Theorem. 172. The three medial lines of a triangle are...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...chord produced to meet a line drawn from the given point through the extremity of the first arc. 7. The perpendiculars from the vertices of a triangle to the opposite sides are the bisectrices of the angles of the triangle formed by joining the feet of the perpendiculars. 8....
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