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What are the reasons for these statements... For example:Statement(AC=BD)Reason(Given)...

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tjjavid | Student, Undergraduate | (Level 1) Honors

Posted March 13, 2013 at 8:09 AM via web

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What are the reasons for these statements...

For example:Statement(AC=BD)Reason(Given)

For example:Statement(AC=AB+BC)Reason(Segment addition postulate)

Statement(AB+BC=BD)Reason?

Statement(BD=BC+CD)Reason?

Statement(AB+BC=BC+CD)Reason?

Statement(AB=CD)Reason?

Statement(CD=AB)Reason?

Statement(Line segment CDcong Line segment AB)Reason?

 

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted March 13, 2013 at 8:48 AM (Answer #1)

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For example:Statement(AC=BD)Reason(Given)

For example:Statement(AC=AB+BC)Reason(Segment addition postulate)

Statement(AB+BC=BD)Reason?

AB+BC=AC   (addition postulate)

AB+BC=BD  ( AC=BD  ) (given)

Statement(BD=BC+CD)Reason?

Segment addition postulate.

 

Statement(AB+BC=BC+CD)Reason?

AB+BC=AC  (Segment addition postulate)

BC+CD=BD (Segment addition postulate)

AC=BD    (given)

Statement(AB=CD)Reason?

AC= BD     (given)

AC-BD=0

AB+BC-(BC+CD)=0

AB-CD=0

AB=CD

 

Statement(CD=AB)Reason?

AC= BD     (given)

BD-AC=0

(BC+CD)-(AB+BC)=0

CD-AB=0

CD=AB

Statement(Line segment CDcong Line segment AB)Reason?

Lenth of line AB= length of line CD ( AB=CD given)

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