 | Joseph Battell - Force and energy - 1903 - 722 pages
...with the diagonal, makes an isosceles triangle, of which half of the other diagonal is the altitude. 'The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.' M "This is only true in an acute or right angle triangle, unless the perpendiculars... | |
 | Olaus Henrici, George Charles Turner - Graphic statics - 1903 - 236 pages
...(or sphere), the sum of the squares on these lines is constant. 1 VECTORS AND ROTORS 134. The three perpendiculars from the vertices of a triangle to the opposite sides are concurrent. OAB is any triangle, let OA=a, OB=p, P the point of intersection of the perpendiculars... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...DP, EQ, FR, of tlie three sides of the A ABC meet in the point 0. QED PROPOSITION XLV. THEOREM 186. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point (called the ortho-center). B Given AD, BF, and CE the perpendiculars from the vertices... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...B. Hence, 0 is equidistant from B and C, and B therefore is in the J- bisector FF'. (Why ?) Ex. 26. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. • A Let the -ls be AH, BP, and CK. Through A, B, C suppose B'C', A'C', A'B', drawn... | |
 | Levi Leonard Conant - Geometry - 1905 - 140 pages
...of the bases of the two parallelograms. 94. The perpendiculars from the vertices of an acuteangled triangle to the opposite sides are the bisectors of...angles of the triangle formed by joining the feet of these perpendiculars. What modification does this theorem undergo in the case of the obtuse-angled... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...bases and equal to half their sum. [This is another form of stating the theorem of 144.] 150. THEOREM The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. Given : A ABC, AX JL to BC, BY -L to AC, and cz -L to AB. To Prove : These three Js... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...length for all positions of point P. [Draw BC. Prove Z BCD, the ext. £ of = a constant. Etc.] 67. The perpendiculars from the vertices of a triangle...bisectors of the angles of the triangle formed by joiuing the feet of these perpendiculars. 112 Proof : If a circle be described on AO as diam., it will... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...bases and equal to half their sum. [This is another form of stating the theorem of 144.] 150. THEOREM. The perpendiculars from the vertices of a triangle to the opposite sides meet in a point. Given : A ABC, AX -L to BC, BY -L to AC, and CZ -l. to AB. To Prove : These three... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...Join O, the point of intersection, with the third vertex C. Prove that OC bisects Z C. 3. Prove that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point. SUGGESTIONS. Through the vertices of the triangle draw lines parallel respectively... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...from A and C.) 136. It follows from § 135 that PLANE GEOMETRY — BOOK I PROP. XL VI. THEOREM 137. The perpendiculars from the vertices of a triangle to the opposite sides intersect at a common point. ,H Draw .any A ABC. From A, B, and C draw lines AD (a), BE (6), and CF... | |
| |
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. 
