Angle Bisectors Perpendicular Bisectors

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

• angle bisector

• perpendicular bisector

• median

• midsegment

A segment that bisects one of the angles of a triangle

• Angle Bisector

• Perpendicular Bisector

• Altitude

• Midsegment

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

• orthocenter

• centroid

• circumcenter

• incenter

If G is the circumcenter, what type of segments are drawn?

• perpendicular bisectors

• angle bisectors

• altitudes

• centroids

∠XOZ is bisected by ray OY. Which statement is true?

• ∠XOZ ≅ ∠XOY

• ∠XOZ ≅ ∠ZOY

• ∠XOY ≅ ∠ZOY

• ∠OXY ≅ ∠OZY

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

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
What is the justification for Step 6?

• Subtraction property of equality

• Substitution

• Addition property of equality

• Definition of congruent angles

Make a statement that MUST be true if you are given an angle bisector.

• EF=FC

• m<EFD+m<DFC=m<EFC

• m<EFD=m<DFC

• m<EFC=m<DFC

What is reason 2?

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