Angle Bisector and Perpendicular Bisector Theorems

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

• angle bisector

• perpendicular bisector

• median

• midsegment

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

• altitude 

• perpendicular bisector

• midsegment

• angle bisector

What is a line segment or ray drawn from a vertex that divides the angle into two congruent angles?

• Median of a Triangle

• Altitude of a Triangle

• Perpendicular Bisector of a side of a Triangle

• Angle Bisector

• Midpoint of a Line Segment

In a triangle what is the line that is drawn perpendicular to a side of a triangle through its midpoint?

• Median of a Triangle

• Altitude of a Triangle

• Perpendicular Bisector of a side of a Triangle

• Angle Bisector

• Midpoint of a Line Segment

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

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

Finish the Perpendicular Bisector Theorem: If CP is the perpendicular bisector of AB, then...

• CA = CB

• AP = PB

• Angle A = Angle B

Use the Perp Bisector Theorem to DC (hint...find x first and then plug it back in to DC)

Mathematical Equivalence

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