tangent and radius are definition of a circle radii bisect chords

tangent and radius are definition of a circle

radii bisect chords

A

B

C

statement reason

AB is tangent to C at B given

given: AB is tangent to C at B 1/5

prove: <A + <C = 90

hint: tangent and radius are

A

B

C

statement reason

AB is tangent to C at B givenAB BC tangent and radius are <B = 90 definition of lines<A + <B + <C = 180 triangle sum theorem<A + 90 + <C = 180 substitution<A + <C = 90 subtraction property

given: AB is tangent to C at B 1/5

prove: <A + <C = 90

hint: tangent and radius are

D

A

B

C

statement reason

AB is tangent to C at B givenAD is tangent to C at D given

given: AB is tangent to C at B 2/5

AD is tangent to C at D

prove: AB = AD

hint: cong tri

D

A

B

C

statement reason

AB is tangent to C at B givenAD is tangent to C at D givenAB BC tangent and radius are AD CD tangent and radius are <CBA = 90 definition of lines<CDA = 90 definition of linesCB = CD definition of a circleCA = CA reflexive property∆ABC = ∆ADC HLAB = AD CPCTC

given: AB is tangent to C at B 2/5

AD is tangent to C at D

prove: AB = AD

hint: cong tri

A

B

C

D

given: DC is diameter of E 3/5

DC AB

prove: AF = BF

hint: draw AE and BE

E

F

statement reason

DC is diameter of E givenDC AB given

A

B

C

D

given: DC is diameter of E 3/5

DC AB

prove: AF = BF

E

F

statement reason

DC is diameter of E givenDC AB givenDraw EA two points determine a lineDraw EB two points determine a line

A

B

C

D

given: DC is diameter of E 3/5

DC AB

prove: AF = BF

E

F

statement reason

DC is diameter of E givenDC AB givenDraw AE two points determine a lineDraw BE two points determine a line<EFA = 90 definition of lines<EFB = 90 definition of linesAE = BE definition of a circleEF = EF reflexive property∆AEF = ∆BEF HLAF = BF CPCTC

given: XB AC, XE FDXB = XE

prove: AC = FD

Hint: draw XC and XD, radii bisect chords (refer to proof #3)

statement reason

XB AC, XE FD givenXB = XE given

4/5

given: XB AC, XE FDXB = XE

prove: AC = FD

Hint: draw XC and XD, radii bisect chords

statement reason

XB AC, XE FD givenXB = XE givenDraw XC and XD two points determine a line<XBC = 90, <XED = 90 definition of linesXC = XD definition of a circle∆XED = ∆XBC HLBC = ED CPCTCAB = BC, ED = FE radii bisect chordsAB = FE substitutionAB + BC = FE + ED addition propertyAC = AB + BC segment addition postulateFD = FE + ED segment addition postulateAC = FD substitution

4/5

given: AB is diameter of D 5/5

prove: <ADC = 2(<B)

hint: base angles thm, ext angles thm

statement reason

AB is diameter of D given

A B

C

D

given: AB is diameter of D 5/5

prove: <ADC = 2(<B)

statement reason

AB is diameter of D givenDB = DC definition of a circle<B = <C base angles theorem<ADC = <C + <B exterior angles theorem<ADC = <B + <B substitution<ADC = 2(<B) combine like terms

A B

C

D