Ch5: Bisectors

Objective: To review the Ideas and concepts of bisectors. To use PAMA

CICO as an effective study tool.College Geometry

Singleton

Midpoints with LSR and Angles with Rays are most common bisectors.

Midpoints and 90˚

Bisector

Perpendicular Bisector

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

Any Ray that divides any Angle into 2 equal parts. The bisector is equidistant to the sides.

Angle Bisector Theorem

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

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

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

9

13

JG

H

E

D F

12 16

P

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 .

________

A

F

B

G

DC

E

40º

m<GCE =

mGF =

m<GEC =

M BG = 3

4