tangent and radius are definition of a circle radii bisect chords
DESCRIPTION
tangent and radius are definition of a circle radii bisect chords. given:AB is tangent to C at B 1/5 prove:TRANSCRIPT
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