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
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