Circle Proofs - HW
Name___________KEY________________Period_________
1.
Statements
Reasons
1 ≅ 1. Given
2 ≅ 2. Reflexive property
3 ≅ 3. Def of Circle
4
4. SSS
∆ ≅ ∆
2. Given: circle O, is tangent to the circle at B,
.
C is the midpoint of Prove: ∠ABC ≅ ∠CBD
Statements
Reasons
1. circle O, is tangent to the circle at
.
B, C is the midpoint of 1. Given
≅ 2. 2. Definition of midpoint
3. 3. Definition of Congruence
4. m∠ABC 3. Inscribed angle theorem
5. m∠CBD 4. Inscribed angle theorem
6. m∠ABC ≅ 5. Substitution
7. ∠ ∠
6. Substitution
8. ∠ABC ≅ ∠CBD
8. Def of ≅
1
3. Given: and are tangent to circle O,
≅ 2
3
4
Prove: ∠AOP ≅ ∠BOP
Statements
Reasons
1. and are tangent to circle O,
≅ 1. Given
2. ≅ 2. All radii are ≅
4. and 4. Tangent Theorem
5. ∠1 and ∠4 are right angles
5. Definition of 6. ∠1 ≅ ∠4
6. All right anglesare≅
7. ∆ ≅ ∆
7. SAS
8. ∠ ≅ ∠
8. CPCTC
4. Given: Circle O, ||
1
3
Prove: ≅ Statements
2
4
Reasons
1. Circle O, ||
1. Given
≅ 2. 2. Parallel lines intercept congruent arcs.
3. ≅ 3. Congruent chords intercept ≅ arcs.
4. ∠1 ≅ ∠2
4. VA ≅
5. ∠3 ≅ ∠4
5. Inscribed angles intercepting the same arc
are ≅
6. ∆BAE ≅ ∆CDE
6. AAS
7. ≅ 7. CPCTC
5. Given: Regular Pentagon ABCDE inscribed in circle O with
and 1
2
3
Prove: and trisects ∠BAE
(cuts into 3)
Statements
1. Regular Pentagon ABCDE inscribed in
circle O with and Reasons
1. Given
2. ≅ ≅ 2. Def of Regular
≅ ≅ 3. 3. Congruent chords intercept ≅ arcs
4. ∠1 ≅ ∠2 ≅ ∠3
4. Inscribed angles intercepting ≅ arcs are ≅
5. and trisects ∠BAE
5. Def of trisect