...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...

...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...

...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...

...(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...

...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...

...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...

...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...

...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...

...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...

...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...