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tangent and radius are  definition of a circle radii bisect  chords

tangent and radius are  definition of a circle radii bisect  chords. given: AB is tangent to  C at B 1/5 prove: <A + <C = 90 hint: tangent and radius are . B. A. C. statement reason AB is tangent to  C at B given. given: AB is tangent to  C at B 1/5

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tangent and radius are  definition of a circle radii bisect  chords

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  1. tangent and radius are  definition of a circle radii bisect  chords

  2. given: AB is tangent to  C at B 1/5 prove: <A + <C = 90 hint: tangent and radius are  B A C statement reason AB is tangent to  C at B given

  3. given: AB is tangent to  C at B 1/5 prove: <A + <C = 90 hint: tangent and radius are  B A C statement reason AB is tangent to  C at B given AB  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

  4. given: AB is tangent to  C at B 2/5 AD is tangent to  C at D prove: AB = AD hint: cong tri B A C D statement reason AB is tangent to  C at B given AD is tangent to  C at D given

  5. given: AB is tangent to  C at B 2/5 AD is tangent to  C at D prove: AB = AD hint: cong tri B A C D statement reason AB is tangent to  C at B given AD is tangent to  C at D given AB  BC tangent and radius are  AD  CD tangent and radius are  <CBA = 90 definition of  lines <CDA = 90 definition of  lines CB = CD definition of a circle CA = CA reflexive property ∆ABC = ∆ADC HL AB = AD CPCTC

  6. D given: DC is diameter of  E 3/5 DC  AB prove: AF = BF hint: draw AE and BE E B F C A statement reason DC is diameter of  E given DC  AB given

  7. D given: DC is diameter of  E 3/5 DC  AB prove: AF = BF E B F C A statement reason DC is diameter of  E given DC  AB given Draw EA two points determine a line Draw EB two points determine a line

  8. D given: DC is diameter of  E 3/5 DC  AB prove: AF = BF E B F C A statement reason DC is diameter of  E given DC  AB given Draw AE two points determine a line Draw BE two points determine a line <EFA = 90 definition of  lines <EFB = 90 definition of  lines AE = BE definition of a circle EF = EF reflexive property ∆AEF = ∆BEF HL AF = BF CPCTC

  9. given: XB  AC, XE  FD XB = XE prove: AC = FD Hint: draw XC and XD, radii bisect  chords (refer to proof #3) 4/5 statement reason XB  AC, XE  FD given XB = XE given

  10. given: XB  AC, XE  FD XB = XE prove: AC = FD Hint: draw XC and XD, radii bisect  chords 4/5 statement reason XB  AC, XE  FD given XB = XE given Draw XC and XD two points determine a line <XBC = 90, <XED = 90 definition of  lines XC = XD definition of a circle ∆XED = ∆XBC HL BC = ED CPCTC AB = BC, ED = FE radii bisect  chords AB = FE substitution AB + BC = FE + ED addition property AC = AB + BC segment addition postulate FD = FE + ED segment addition postulate AC = FD substitution

  11. C given: AB is diameter of  D 5/5 prove: <ADC = 2(<B) hint: base angles thm, ext angles thm A B D statement reason AB is diameter of  D given

  12. C given: AB is diameter of  D 5/5 prove: <ADC = 2(<B) A B D statement reason AB is diameter of  D given DB = DC definition of a circle <B = <C base angles theorem <ADC = <C + <B exterior angles theorem <ADC = <B + <Bsubstitution <ADC = 2(<B)combine like terms

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