Problem

Supply reasons.Given: intersects at O so that ∠1 is a right ∠ (Use the figure following E...

Supply reasons.

Given:	intersects at O so that ∠1 is a right ∠ (Use the figure following Exercise 1.)
Prove:	∠2 and ∠3 are complementary

PROOF
Statements	Reasons
1. intersects at O	1. ?
2. ∠AOB is a straight ∠, so m ∠ AOB = 180	2. ?
3. m∠1 + m∠COB = m∠AOB	3. ?
4. m∠1 + m∠COB = 180	4. ?
5. ∠1 is a right angle	5. ?
6. m∠1 = 90	6. ?
7. 90 + m∠COB = 180	7. ?
8. m∠COB = 90	8. ?
9. m∠2 + m∠3 = m ∠ COB	9. ?
10. m∠2 + m∠3 = 90	10. ?
11. ∠2 and ∠3 are complementary	11. ?

In Exercises 3 and 4, supply statements.

Exercise 3

Supply reasons.

Given:	∠1 ≅ ∠3
Prove:	∠MOP ≅ ∠NOQ

PROOF
Statements	Reasons
1. ∠1 ≅ ∠3	1. ?
2. m∠1 = m∠3	2. ?
3. m∠1 + m∠2 = m∠MOP and m∠2 + m∠3 = m ∠NOQ	3. ?
4. m∠1 + m∠2 = m∠2 + m∠3	4. ?
5. m∠MOP = m∠NOQ	5. ?
6. ∠MOP ≅ ∠NOQ	6. ?

Exercise 2

Exercise 3

Supply reasons.

Given:	∠1 ≅ ∠2 and ∠2 = ∠3
Prove:	∠1 ≅ ∠ 3

(Use the figure following Exercise 1.)

PROOF
Statements	Reasons
1. ?	1. Given
2. ?	2. Transitive Property of Congruence

Exercise 4

Supply reasons.
Given:
∠1 ≅ ∠3
Prove:
∠MOP ≅ ∠NOQ
PROOF
Statements
Reasons
1. ∠1 ≅ ∠3
1. ?
2. m∠1 = m∠3
2. ?
3. m∠1 + m∠2 = m∠MOP and m∠2 + m∠3 = m ∠NOQ
3. ?
4. m∠1 + m∠2 = m∠2 + m∠3
4. ?
5. m∠MOP = m∠NOQ
5. ?
6. ∠MOP ≅ ∠NOQ
6. ?
Exercise 2
Exercise 3
Supply reasons.
Given:
m∠AOB = m∠1
m∠BOC = m∠1
Prove:
OB bisects ∠AOC
PROOF
Statements
Reasons
1. ?
1. Given
2. ?
2. Substitution
3. ?
3. Angles with equal measures are congruent
4. ?
4. If a ray divides an angle into two congruent angles, then the ray bisects the angle