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Given: m∠DBA=45°; m∠DEB=45°; Prove: ∠DBC ≅ ∠FEB
1. ∠DBA and ∠DBC are supplementary 1. they form a linear
pair.
2. m∠DBA + m∠DBC = 180° 2. the measures of
supplementary
angles total 180°
3. m∠DBA = 45° 3. Given
4. 45° + m∠DBC = 180° 4. Equals may be
substituted for
equals
5. m∠DBC = 135° 5. Equals 45° may be
subtracted from
equals
6. ∠DEB and ∠FEB are supplementary 1. they form a linear
pair.
2. m∠DEB + m∠FEB = 180° 2. the measures of
supplementary
angles total 180°
3. m∠DEB = 45° 3. Given
4. 45° + m∠FEB = 180° 4. Equals may be
substituted for
equals
5. m∠FEB = 135° 5. Equals 45° may be
subtracted from
equals
6. ∠DBC ≅ ∠FEB 6. Angles with equal
measures are
congruent.
Edwin
