Perpendicular Bisector Angle Bisector Robyn

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

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

• perpendicular bisectors

• angle bisectors

• altitudes

• centroids

The point of concurrency of the 3 perpendicular bisectors of a triangle is called the ___?

• Midsegment

• Incenter

• Circumcenter

• Centriod

In the given proof, what is the statement for step 2?

What is reason 1?

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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

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

Mathematical Equivalence

ON

What is reason 2?

• 
• 
• 
• 

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
What is the justification for Step 4?

• Given

• Substitution

• Angle addition postulate

• Definition of congruent angles