Triangle Proportionality with Angle Bisectors
- Anthony DiLaura
Change the line BF to become the angle bisector of angle B in triangle CBD. Change the measure of angle B and the vertices of the triangle to discover how the angle bisector creates proportional segments in a triangle.
Questions: 1) As Point F becomes closer to the red dot on segment CD what do you notice about the two angles formed at angle B in the triangle? What does this make line BF to angle B? 2) When BF is the angle bisector of angle B what is true about the proportions on the side of the sketch? 3) Describe the ratios that are equal when BF is the angle bisector. In other words, describe the segments that are being used in the ratios numerator and denominator. 4) What is true about the ratios of these segments when point F is not on the red dot on side DC? Why?