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Given: Quadrilateral ABCD is inscribed in circle O. 

Prove: mA+mC=180dg

Fill in the blanks(___) to complete the proof.

 

Statements:                                                                        Reason:

Quadrilateral ABCD is inscribed in circle O.                        Given     

m(arc)BCD=2(mA)                                                              1._____ 

2._____                                                                                 Inscribed Angle Theorem 

m(arc)BCD+m(arc)DAB=360dg                                           3.____

2(mA)+2(mC)=360dg                                                          Substitution Property

4._____                                                                                  Division Property of Equality

 

Here are the options: Inscribed Angle Theorem, The sum of the arcs that make a circle is 360dg, Central Angle Theorem, mA+mB=180dg, mA+mC=180dg, and m(arc)DAB=2(mC). 

Guest Mar 22, 2017
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1. Inscribed Angle Theorem

2. m(arc)DAB=2(mC)

3. The sum of the arcs that make a circle is 360dg, 

4. mA+mC=180dg

 

In Hong Kong we just do "opp.(opposite) angles of cyclic quadrilateral" and then write mA + mC = 180. All finished. :)

MaxWong  Mar 22, 2017

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