Four Centers of a Triangle Answers Name KEY For questions 1 – 6 ...

Four Centers of a Triangle AnswersName KEYFor questions 1 – 6, choose the best answer.1. Which point of concurrency is shown in thediagram?3. Which triangle's center is never outside thetriangle?(1) orthocenter only(2) incenter only(3) both orthocenter and circumcenter(4) both incenter and centroid4. Find JN .(1) centroid(2) circumcenter(3) incenter(4) orthocenter2. Which point of concurrency is shown in thediagram?(1) centroid(2) circumcenter(3) incenter(4) orthocenter(1) 16 cm(2) 12 cm(3) 513 cm(4) 4 cm5. The altitudes of a triangle are concurrent at apoint called the(1) centroid(2) circumcenter(3) incenter(4) orthocenter6. The medians of a triangle are concurrent at apoint called the(1) centroid(2) circumcenter(3) incenter(4) orthocenterComplete each statement using always, sometimes or never.7. A perpendicular bisector of a triangle _____________ ALWAYS passes through the midpoint of a side of the triangle.8. The angle bisectors of a triangle _____________ ALWAYS intersect at a single point.9. The angle bisectors of a triangle _____________ NEVER meet at a point outside the triangle.10. The circumcenter of a triangle _____________ SOMETIMES lies outside the triangle.

For #11 – 14, find the indicated measure.11. The perpendicular bisectors of RST meet atpoint D. Find DR .CircumcenterDR = 913. The angle bisectors of GHJ meet at point K.Find KB .IncenterKB = 312. The angle bisectors of XYZ meet at point W.Find WB .14. The perpendicular bisectors of MNP meet atpoint Q. Find QN .IncenterWB = 20CircumcenterQN = 25For # 15 – 18, use the given figure and information:P is the centroid of DEF . EH ⊥ DF , DH = 9 , DG = 7.5 , EP = 8 and DE = FE .15. Find the length of FH . 97.51516. Find the length of EH . 12CentroidEP:PH=2:14917. Find the length of PH . 418. Find the perimeter of DEF . 482 29 + 12 =81+ 144 =225 =( EF )( EF )2( EF )22EF = 15