2F Mastering Tools of Geometry Name______________________________________ 1. What is the difference between and angle bisector and a perpendicular bisector? 2. What is the difference between a perpendicular bisector and an altitude? 3. What is the difference between a perpendicular bisector and a median? 4. Could a median be a perpendicular bisector of a side of a triangle? Justify your response. 5-­‐7: Use the triangle. 5. What special segment is EB for ΔABC? 6. What special segment is AD for ΔABC? 7. If CF were both an angle bisector and an altitude of ΔABC, what kind triangle would ΔABC have to be? 8. Which point of concurrency is the center of the circumscribed circle for the triangle? 9. Which point of concurrency is the center of mass for the triangle? 10. Which point of concurrency is located on the right angle of a right triangle? 11. What is special about the incenter of a triangle? 12. Which special segments intersect at the orthocenter of a triangle? 13. Which special segments intersect at the circumcenter of a triangle? 14. Which special segments intersect at the incenter of a triangle? 15-­‐19: Draw and label a sketch to illustrate each situation. 15. !PS is a median of ΔPQR. 18. AC and BC are altitudes of ΔABC. 16. !QT is an angle bisector of ΔPQR. 19. !DX is an altitude of ΔDEF, and X is between E and F. 17. !RU is an altitude of ΔPQR, and Q is between U and P. 20. Given: !AD is an altitude of ΔABC, CD=(x+7), BD=(2x–15), and m∠ADC=(4x–6)°. What are the values of x and BC? 21. Given: PS is a median of ΔPQR, SQ=(5x+3), SR=(10x–7), and m∠PSQ=(15x+42)°. What are the values of x and m∠PSR? 22. Given: !YV is an angle bisector of ΔXYZ. Determine m∠ZYV and m∠XYZ if m∠XYZ=(8x–6)° and m∠XYV=(2x+7)°. 23. Given: BD is an angle bisector of ΔABC. IF FG=(2x+6) and 24. Given: !SU is a median of ΔRST. If TU=(2x+24) and EF=(4x–1), what are the values of x and EF? RU=(5x–30), what are the values of x and RT? 25. If C is the centroid of ΔAXY, AB=36, CY=16 and CD=10, what is AC? 27. If possible, classify ΔXYZ. Explain your reasoning. Note: Diagram not necessarily to scale. 26. In the diagram, XC=36, CE=30, and FZ=56. What is CY? 28. If possible, classify ΔXYZ. Explain your reasoning. Note: Diagram not necessarily to scale.