3.4 Basic Constructions Justified

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3.4 Basic Constructions Justified

• Justify Method for Constructing an Angle
  Congruent to a given Angle. Ex. 1 p. 154
• Given ?ABC
• BD ? BE ? ST ? SR (by construction)
• DE ? TR (by construction)
• Prove ?B ? ?S
• PROOF
• Statements Reasons
• ?ABC_ __ __ 1. Given
• BD ? BE ? ST ? SR (by construction)
• DE ? TR (by construction)
• ?EBD ? ?RST 2. SSS
• 3. ?B ? ?S 3. CPCTC
• Ex 2 p.154

? ? ? ? ? ?
? ? ? ? ? ?
2
Justify Method for Constructing the Bisector of
an Angle

• Given ?XYZ
• YM ?YN (by construction)
• MW ?NW (by construction)
• Prove YW bisects ?XYZ
• PROOF
• Statements Reasons
• ?XYZ YM ?YN MW ?NW 1. Given
• YW ? YW 2. Identity
• ?YMW ? ?YNW 3. SSS
• ?MYW ? ? NYW 4. CPCTC
• YW bisects ?XYZ 5. Definition of bisector
• Ex. 4 Using this construction, construct a 30
  degree angle.

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3
Justify Construction for a line perpendicular
to a given line from a point not on that line

• Given P not on l
• PA ? PB( by construction)
• AQ ? BQ (by construction)
• Prove PQ ? AB
• PROOF
• Statements Reasons
• 1. P not on l __ 1. Given
• PA ? PB AQ ? BQ
• PQ ? PQ 2. Identity
• ?PAQ ? ?PBQ 3. SSS
• ?1 ? ?2 4. CPCTC
• PR ?PR 5. Identity
• ?PRA ? ?PRB 6. SAS
• ?3 ? ?4 7. CPCTC
• PQ ? AB 8. If two lines meet to form ? adjacent
  ?s, these lines are ?
• Ex. 6 p. 156 Construct a 45 degree angle.

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