 | James Howard Gore - Geometry - 1899 - 266 pages
...are severally equal. 4. The perpendiculars from the angles upon the opposite sides of the triangle are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars. 5. A straight line will cut a circle, or lie entirely without it, according as its distance from the... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...and b, Prop. XLII .'. P1 lies on CT. Similarly for P , . Prop. XLII PROPOSITION XLV. 133. Theorem. The perpendiculars from the vertices of a triangle to the opposite sides are concurrent. Given the A ABC. To prove that the perpendiculars from A, B, C, to a, b, c, respectively,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...case of prop. XXXI : The perpendicular bisectors of the sides of a triangle are concurrent. 510. Also, the perpendiculars from the vertices of a triangle to the opposite sides are concurrent. 511. If three circumferences intersect in pairs, the common chords are concurrent. 512.... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...B. Hence, 0 is equidistant from B and C, and B therefore is in the _L bisector FF'. (Why ?) Ex. 26. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. Let the Js be AH, BP, and CK. Through A, B, C suppose B'C', A'fT, A'R, drawn II to... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
...through the feet of the perpendiculars from the other vertices to the opposite sides. 295. Prove that the perpendiculars from the vertices of a triangle to the opposite sides bisect the angles of the triangle formed by joining their feet ; the so-called Pedal Triangle. PROPOSITION... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...interior angles of a parallelogram form a rectangle. RECTILINEAR FIGURES. 63 PROP. LI. THEOREM. 138. The perpendiculars from the vertices of a triangle to the opposite sides intersect at a common point. Given AD, BE, and CFfhe Js from the vertices of A ABC to the opposite... | |
 | William James Milne - Geometry - 1899 - 396 pages
...from the vertices perpendicular to the opposite sides. Do these lines intersect in a point? Theorem. The perpendiculars from the vertices of a triangle to the opposite sides pass through the same point. H c Data: Any triangle, as ABC, and the lines AD, BE, and CF drawn from... | |
 | New York (State). Department of Public Instruction - Education - 1900 - 1314 pages
...examples of two of them. 2 Give two theorems upon the equality of triangles, and prove your second. S The perpendiculars from the vertices of a triangle to the opposite sides meet in a 682 Department of Public Instruction 6 Prove that two triangles are similar when the sides... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...the points of contact. 12. The perpendiculars from the angles upon the opposite sides of a triangle are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars. 13. The bisectors of the vertical angles of all triangles having a commou base and equal vertical angles... | |
 | Perspective - 1902 - 132 pages
...picture plane. SPa will be vertically in line with SPr at a distance from HPP equal to rs. 133. — Since the perpendiculars from the vertices of a triangle to the opposite sides meet in a common point, it is evident that any three points may represent the vanishing points of three... | |
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The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars. 
