Angular Bisector Theorem

Find the missing length.

• 8

• 7

• 20

• 40

Find the missing length.

• 12

• 10

• 16

• 5

Find the missing length.

• 10

• 21

• 35

• 9

Find the missing length.

• 25

• 15

• 6

• 16

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

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

∠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
What is the justification for Step 7?

• Subtraction property of equality

• Transitive property of equality

• Addition property of equality

• Definition of congruent angles

What is the justification?

• Definition of an Angle Bisector

• Complementary Angles Theorem

• Definition of a Right Angle

• Angle Addition Postulate