definition of a midpoint definition of an angle bisector

A B C Given: B is midpoint of AC Prove: AB = BC Statement Reason B is midpoint of AC given

A B C Given: B is midpoint of AC Prove: AB = BC Statement Reason B is midpoint of AC given AB = BC definition of midpoint

A B C Given: B is midpoint of AC Prove: AC = 2(BC) Statement Reason B is midpoint of AC given

A B C Given: B is midpoint of AC Prove: AC = 2(BC) Statement Reason B is midpoint of AC given AB = BC definition of midpoint

A B C Given: B is midpoint of AC Prove: AC = 2(BC) Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate

A B C Given: B is midpoint of AC Prove: AC = 2(BC) Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate AC = BC + BC substitution

A B C Given: B is midpoint of AC Prove: AC = 2(BC) Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate AC = BC + BC substitution AC = 2(BC) combine like terms

A B C Given: B is midpoint of AC Prove: BC = (1/2)AC Statement Reason B is midpoint of AC given

A B C Given: B is midpoint of AC Prove: BC = (1/2)AC Statement Reason B is midpoint of AC given AB = BC definition of midpoint

A B C Given: B is midpoint of AC Prove: BC = (1/2)AC Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate

A B C Given: B is midpoint of AC Prove: BC = (1/2)AC Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate AC = BC + BC substitution

A B C Given: B is midpoint of AC Prove: BC = (1/2)AC Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate AC = BC + BC substitution AC = 2(BC) combine like terms

A B C Given: B is midpoint of AC Prove: BC = (1/2)AC Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate AC = BC + BC substitution AC = 2(BC) combine like terms (1/2)AC = BC division property

A B C Given: B is midpoint of AC Prove: BC = (1/2)AC Statement Reason B is midpoint of AC given AB = BC definition of midpoint AC = AB + BC segment addition postulate AC = BC + BC substitution AC = 2(BC) combine like terms (1/2)AC = BC division property BC = (1/2)AC symmetric property

A B Given: BD bisects <ABC Prove: <1 = <2 <1 <2 D C Statement Reason BD bisects <ABC given

A B Given: BD bisects <ABC Prove: <1 = <2 <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector

A B Given: BD bisects <ABC Prove: <ABC = 2(<1) <1 <2 D C Statement Reason BD bisects <ABC given

A B Given: BD bisects <ABC Prove: <ABC = 2(<1) <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector

A B Given: BD bisects <ABC Prove: <ABC = 2(<1) <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate

A B Given: BD bisects <ABC Prove: <ABC = 2(<1) <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate <ABC = <1 + <1 substitution

A B Given: BD bisects <ABC Prove: <ABC = 2(<1) <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate <ABC = <1 + <1 substitution <ABC = 2(<1) combine like terms

A B Given: BD bisects <ABC Prove: <1 = (1/2)<ABC <1 <2 D C Statement Reason BD bisects <ABC given

A B Given: BD bisects <ABC Prove: <1 = (1/2)<ABC <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector

A B Given: BD bisects <ABC Prove: <1 = (1/2)<ABC <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate

A B Given: BD bisects <ABC Prove: <1 = (1/2)<ABC <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate <ABC = <1 + <1 substitution

A B Given: BD bisects <ABC Prove: <1 = (1/2)<ABC <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate <ABC = <1 + <1 substitution <ABC = 2(<1) combine like terms

A B Given: BD bisects <ABC Prove: <1 = (1/2)<ABC <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate <ABC = <1 + <1 substitution <ABC = 2(<1) combine like terms (1/2)<ABC = <1 division property

A B Given: BD bisects <ABC Prove: <1 = (1/2)<ABC <1 <2 D C Statement Reason BD bisects <ABC given <1 = <2 definition of angle bisector <ABC = <1 + <2 angle addition postulate <ABC = <1 + <1 substitution <ABC = 2(<1) combine like terms (1/2)<ABC = <1 division property <1 = (1/2)<ABC symmetric property