Mid Segment and Angle Bisector

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

• angle bisector

• perpendicular bisector

• median

• midsegment

The mid segment of the triangle is 5x-1. Find the value of x.

• x = 6

• x = 7

• x = 11.8

• x = 12.4

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

The segment that connects the midpoints of two sides of a triangle is the _________.

• midsegment

• perpendicular bisector

• median

• altitude

• m∠GHK=26, m∠KHJ=26
• m∠GHK=26, m∠KHJ=52
• m∠GHK=52, m∠KHJ=52
• m∠GHK=52, m∠KHJ=26

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

• x=3/17
• x=9
• x=3
• x= -3

• x=67
• x=43
• x=55
• x=12

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

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
What is the justification for Step 6?

• Subtraction property of equality

• Substitution

• Addition property of equality

• Definition of congruent angles