2.5 Perpendicular Lines (Written Exercises)
x = 13
10. Ray BE ⊥ line AC and ray BD ⊥ ray BF. Find the value of x when m∠DBE = 3x, m∠EBF = 4x-1
x = 20
11. Ray BE ⊥ line AC and ray BD ⊥ ray BF. Find the value of x when m∠ABD = 3x-12, m∠DBE= 2x+2, m∠EBF = 2x+8
x = 9
12. Ray BE ⊥ line AC and ray BD ⊥ ray BF. Find the value of x when m∠ABD=6x, m∠DBE=3x+9, m∠EBF=4x+18, m∠FBC=4x
Definition of perpendicular lines
3. What definition or theorem justifies the following statement: If ∠EBC is a right angle, then ray BE ⊥ line AC
Definition of perpendicular lines
4. What definition or theorem justifies the following statement: If line AC ⊥ ray BE, then ∠ABE is a right angle
If the exterior sides of 2 adjacent angles are perpendicular, then the angles are complementary
5. What definition or theorem justifies the following statement: If ray BE ⊥ line AC, then ∠ABD and ∠DBE are complementary.
Definition of complementary angles
6. What definition or theorem justifies the following statement: If ∠ABD and ∠DBE are complementary angles, then m∠ABD + m∠DBE = 90
Def of perpendicular lines
7. What definition or theorem justifies the following statement: If ray BE ⊥ line AC, then m∠ABE=90
If 2 lines form ≅ adjacent angles, then the lines are ⊥
8. What definition or theorem justifies the following statement: If ∠ABE ≅ ∠EBC, then line AC ⊥ ray BE
x = 35
9. Ray BE ⊥ line AC and ray BD ⊥ ray BF. Find the value of x when m∠ABD = 2x-15 and m∠DBE = x
