Center Angle Bisector

The INCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

The place where all three angle bisectors meet is called the ...

• Circumcenter

• Orthocenter

• Incenter

• Centroid

The figure is an example of a(n) ...

• angle bisector

• perpendicular bisector

• median

• midsegment

What type of center is point M?

• Circumcenter

• Incenter

• Centroid

• Orthocenter

If S is the incenter, what type of segments are drawn?

• medians

• angle bisectors

• perpendicular bisectors

• altitudes

Angle JHG measures 161.

• m∠GHK=80.5,

  m∠KHJ=161

• m∠GHK=161,

  m∠KHJ=80.5

• m∠GHK=80.5,

  m∠KHJ=80.5

• m∠GHK=161,

  m∠KHJ=161

Given: m∠LAN = 30⁰ , m∠1 = 15⁰
Prove: AM bisects ∠LAN
Step 1: m∠LAN = 30⁰ 
Step 2: m∠1 + m∠2 = m∠LAN
Step 3: m∠1 + m∠2 = 30⁰
Step 4: m∠1 = 15⁰
Step 5: 15⁰ + m∠2 = 30⁰
Step 6: m∠2 = 15⁰
Step 7: m∠1 = m∠2
Step 8: ∠1 ≅ ∠2
Step 9: AM bisects ∠LAN
What is the justification for Step 9?

• Symmetric property of congruence

• Definition of angle bisector

• Addition property of equality

• Definition of congruent angles

What is the missing statement in the proof?

• 2m∠ABD=m∠ABD+m∠ABD

• m∠ABD=m∠DBC

• m∠ABC=m∠ABC

• m∠ABD+m∠ABD=m∠ABD+m∠DBC

What is the missing statement in the proof?

• 2m∠ABD = m∠ABD + m∠ABD

• m∠ABD = m∠DBC

• m∠ABC = m∠ABC

• m∠ABD +m∠ABD = m∠ABD + m∠DBC

The point of concurrency made by 3 angle bisectors is known as the

• orthocenter

• centroid

• circumcenter

• incenter