Angle Bisectors and Proportionality
AD bisects angle BAC. Drag points B and C to manipulate the diagram. The spreadsheet at the right shows the lengths of the sides AB, AC, BD, and CD as well as the ratios.
1. Are the ratios AB/BD and AC/CD always equal?
2. How can you make AB/BD and AC/CD lower? Hint: What kind of angle at A - acute, obtuse, or right - makes this ratio lower?
3. How can you make AB/BD and AC/CD higher? Hint: What kind of angle at A - acute, obtuse, or right - makes this ratio higher?
4. Are triangles ADB and ADC similar?