...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....

...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....

...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...

...— |- 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....

...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...

...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...

...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...

...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...

...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...

...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....