Angle Bisector Proportional Sides

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

• angle bisector

• perpendicular bisector

• median

• midsegment

Find the value of x

• x=28

• x=14

• x=23

• x=46

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

• angle bisector

• perpendicular bisector

• median

• midsegment

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

Which of the following below would fill in the Reasons in the proper order?

• Given; Definition of bisect; Transitive; Given, Definition of bisect

• Given; Transitive; Given; Definition of bisect; Definition of bisect

• Given; Definition of bisect; Given; Definition of bisect; Transitive

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

If DB bisects ∠ABC, then ∠ABD = ∠CBD.

• Definition of Congruent Angles

• Definition of Angle Bisector

• Angle Addition Postulate

• Definition of Right Angle

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
What is the justification for Step 8?

• Symmetric property of congruence

• Transitive property of equality

• Addition property of equality

• Definition of congruent angles

Identify the center.

• Circumcenter

• Incenter

• Centroid

• Orthocenter