Midsegment and Angle Bisector Theorems

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

• angle bisector

• perpendicular bisector

• median

• midsegment

QR is a midsegment of triangle WUV. What is the length of segment QR?

• 4

• 8

• 16

• 32

QR is a midsegment of triangle WXY. What is the length of segment WY?

• 3

• 6

• 9

• 12

QR is a midsegment of triangle FGH. Solve for the value of x?

• 5.5

• 11

• -5.5

• -11

• A
• B
• C
• D

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
What is the justification for Step 5?

• Given

• Substitution

• Angle addition postulate

• Definition of congruent angles

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