SOLUTION: Can you please help me with the following problem <<<<< write a paragraph proof for theorem 6-6 >>>>> theorem 6-6 states that if both pairs of opposite

Question 173897This question is from textbook Geometry
: Can you please help me with the following problem <<<<< write a paragraph proof for theorem 6-6 >>>>> theorem 6-6 states that if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
THANK YOU!!!! :] This question is from textbook Geometry

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!



.......................................................................

            statement                           reason


1. angle Q congruent to angle S           1. Given
   angle R congruent to angle T 

2. angles Q+R+S+T =360 d                  2.sum of the angles theorem

3. angles R+R+S+S= 360 d                  3. subsitution post.

4. angles 2R+2S  = 360 d                  4. addition post.

5. angles R + S  = 180 d                  5. div. post.

6. angles T + S  = 180 d                  6. subst. post.
   angles T + Q  = 180 d
   angles R + Q  = 180 d
 
7. QRST is a parallelogram                7. if the consecutive angles of a quad
                                             rilateral are supplementary the 
                                             quad is a parallelogram

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