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Statement Reason
1. Given
2. Chords that intercept congruent arcs are congruent
Example 1
CDAB 1.
DCAB 2.
3. All radii of a circle are congruentOCOBOAOD and 3.
CDOABO 4. SSSSSS 4.
Statement Reason
1. Given
2. Vertical angles are congruent
Example 2
OCDAB at intersects 1.
BODAOC 2.
3. All radii of a circle are congruent
DOCO
BOAO
3.
DOBCOA 4. SASSAS 4.
BDCA 5. CPCTC .5
Statement Reason
1. Given
Example 3
3. Angles with a vertex at the center of a circle are central angles.angles central are
and 3. BODAOC
OCDAB at intersects 1.
BODAOC 2. 2. Vertical angles are congruent
4. Congruent central angles intercept congruent arcs.
BDAC 4.
Statement Reason
1. Given
Example 4
FEDE 1.
2. All radii of a circle are congruentOFOD 2.
FOEDOE 4. SSSSSS 4.
3. Reflexive postulateOEOE 3.
Statement Reason
1. Given
2. Congruent chords intercept congruent arcs
Example 5
PRPQ 1.
PRP Q 2.
QRQR 3. 3. Reflexive Postulate
QRPRQRPQ 4. 4. Addition postulate
PRQQRPR
PQRQRPQ
5. 5. Partition postulate
PRQPQR 6. 6. Substitution postulate
Statement Reason
1. Given
2. Perpendicular segments form right angles
Example 6
ABDOC 1.
anglesright are 2 and 1 2.
3. All right angles are congruent21 3.
BDCADC 7. SASSAS 7.
4. Reflexive postulateDCDC 4.5. A diameter perpendicular to a chord bisects the chord.
BACD bisects 5.
6. A segment bisector divides a segment into 2 congruent parts.
DABD 6.
ACBC 8. CPCTC 8.
Statement Reason
1. Given
2. Vertical angles are congruent
Example 7
CDAB 1.
21 2.
DB 3.
AASAAS 4.
3. Inscribed angles that intercept the same arc are congruent.
CDEABE 4.
Statement Reason
1. Given
2. Chords that intercept congruent arcs are congruent
Example 8
CDAB 1.
DCAB 2.
DCBABC 9. SASSAS 9.
BCACBD 3. 3. Inscribed angles that intercept congruent arcs are congruent.
DCAABD 4. 4. Inscribed angles that intercept the same arc are congruent.
DCABCAABDCBD 5. 5. Addition postulate
6. Partition postulate
7. Substitution postulate
BCDDCABCA
CBAABDCBD
6.
BCDCBA 7.
BCBC 8. 8. Reflexive Postulate
Example 2
Statement Reason
Example 2
Statement Reason
Statement Reason
Example 2
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