Ch5: Bisectors

1. Ch5: Bisectors Objective: To review the Ideas and concepts of bisectors. To use PAMA CICO as an effective study tool. College Geometry Singleton

2. Definitions Midpoints with LSR and Angles with Rays are most common bisectors. Midpoints and 90˚ • Bisector • Perpendicular Bisector

3. Definitions Any Ray that divides any Angle into 2 equal parts. LSR that is 90˚ to another LSR and intersecting the Midpoint. The endpoints are equidistant to the vertex • Angle Bisector Perpendicular Bisector Theorem

4. Definitions Any Ray that divides any Angle into 2 equal parts. The bisector is equidistant to the sides. • Angle Bisector Theorem

5. Definitions The point of concurrency of the perpendicular bisectors. The circumcenter is equidistant to the vertices. The point of concurrency of the angle bisectors. The incenter is equidistant to the sides at 90. • Circumcenter Incenter

6. Definitions The point of concurrency of the Medians. The Centroid is the 2/3 rule. The point of concurrency of the altitudes. The orthocenter is inside when triangle is acute, outside when triangle is obtuse and on the 90˚ vertex when Right. • Centroid Orthocenter

7. PAMA CICO • P – Perp. bisector • A – Angle Bisectors • M - Medians • A - Altitudes • C – Circumcenter – equidistant to the Corners! • I – Incenter – equidistant to the Sides! • C – 2/3 of the median is from vertex to centroid. • O - Orthocenter

8. E 12 16 G J 9 P D F 13 H Centroid Example P is the centroid of ∆DEF, Find the length of EH. ________ Find the length of DE. ________ Find the length of DP. ________ Find the perimeter of ∆DEF . ________

9. A F E G C B D 40º G is the Incenter of ∆ABC 3 4 m<GCE = mGF = m<GEC = M BG =