1. Lesson 2-5 Perpendicular Lines (page 56)
Essential Question
Can you justify the conclusion of a conditional statement?

2. Perpendicular Lines

3. Perpendicular Lines (⊥-lines):
… two lines that intersect to form right angles.
Example: m n

4. then _____, _____, _____, and _____ are right angles.
Example:
If m ⊥n,
then _____, _____, _____, and _____ are right angles. ∠1 ∠2 ∠3 ∠4 1 2 m 4 3 n
How many angles must be right angles in
order for the lines to be perpendicular? _____ 1

5. Theorem 2-4 ⊥-lines ⇒ ≅ adj∠’s
If two lines are perpendicular, then they form congruent adjacent angles.
Given: l ⊥ n
Prove: ∠1, ∠2, ∠3, & ∠4
are congruent angles. l 2 1 n 3 4

6. See page 57 Classroom Exercises #1.
Given: l ⊥ n
Prove: ∠1, ∠2, ∠3, & ∠4
are congruent angles. 2 1 n 3 4
See page 57
Classroom Exercises
#1.
Statements Reasons
___________________ ___________________
___________________ ___________________

7. Note: This is the converse of Theorem 2-4.
2 lines form ≅ adj∠’s
⇒⊥-lines
Theorem 2-5
If two lines form congruent adjacent angles, then they are perpendicular .
Given: ∠1 ≅ ∠2
Prove: l ⊥ n l 2 1 n
Note: This is the converse of Theorem 2-4.

8. Given: ∠1 ≅ ∠2 Prove: l ⊥ n ___________________ ___________________
See page 58
Written Exercises
#2!
Statements Reasons
___________________ ___________________
______________________ ___________________

9. Theorem 2-6 Ext S 2 adj A∠’s ⊥ ⇒ comp ∠’s
If the exterior sides of two adjacent acute angles are perpendicular , then the angles are complementary. A •
Given:
Prove: ∠AOB and ∠BOC
are comp. ∠‘s B • • O C

10. Given: Prove: ∠AOB and ∠BOC ___________________ ___________________•
Given:
Prove: ∠AOB and ∠BOC
are comp. ∠‘s B • • O C
See page 59
Written Exercises
#13.
Statements Reasons
___________________ ___________________
______________________ ___________________

11. Example:. Name the definition or theorem that justifies
Example: Name the definition or theorem that justifies each statement about the diagram. B 1 2 3 4 A C 5 6 8 7 D
(a)
_________________________________
Def. of ⊥-lines

12. Example:. Name the definition or theorem that justifies
Example: Name the definition or theorem that justifies each statement about the diagram. B 1 2 3 4 A C 5 6 8 7 D
(b)
_________________________________
⊥-lines ⇒ ≅ adj∠’s

13. Ext S 2 adj A∠’s ⊥ ⇒ comp ∠’s
Example: Name the definition or theorem that justifies each statement about the diagram. B 1 2 3 4 A C 5 6 8 7 D
(c)
_________________________________
Ext S 2 adj A∠’s ⊥ ⇒ comp ∠’s

14. Def. of comp ∠’s then m∠7 + m∠8 = 90º.
Example: Name the definition or theorem that justifies each statement about the diagram. B 1 2 3 4 A C 5 6 8 7 D
(d) If ∠7 & ∠8 are complementary,
then m∠7 + m∠8 = 90º.
_________________________________
Def. of comp ∠’s

15. 2 lines form ≅ adj∠’s ⇒⊥-lines
Example: Name the definition or theorem that justifies each statement about the diagram. B 1 2 3 4 A C 5 6 8 7 D
(e)
_________________________________
2 lines form ≅ adj∠’s ⇒⊥-lines

16. Example:. Name the definition or theorem that justifies
Example: Name the definition or theorem that justifies each statement about the diagram. B 1 2 3 4 A C 5 6 8 7 D
(f) ∠4 ≅ ∠5.
_________________________________
Vertical ∠’s R ≅

17. Example:. Name the definition or theorem that justifies
Example: Name the definition or theorem that justifies each statement about the diagram. B 1 2 3 4 A C 5 6 8 7 D
(g) If ∠ABC is a right angle,
then m∠ABC = 90º.
_________________________________
Def. of Rt. ∠

18. 65º+25º = 90º 13 Example. If ZW ⊥ ZY, m∠1 = 5x, and m∠2 = 2x - 1,
find the value of x. 13
x = ______ W • V • 1 2 • Z Y
65º+25º
= 90º

19. Can you justify the conclusion of a conditional statement?
Assignment
Written Exercises on pages 58 & 59
GRADED: 3 to 12 ALL numbers
GROUP WORK: 19 to 25 odd numbers
Can you justify the conclusion of a conditional statement?
Prepare for a quiz on
Lesson 2-2 to 2-5: Justifications
AFTER lesson 2-6!