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Home > GC > Chapter 7 > Lesson 7.2.5 > Problem 7-85

7-85.

What else can you prove about parallelograms? Prove that if a pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral must be a parallelogram. For example, for the quadrilateral below, given that and , show that . Organize your reasoning in a flowchart. Then record your theorem in your Theorem Toolkit (Lesson 7.2.1A Resource Page).

Quadrilateral A, B, C, D. Side A, B and side C, D are both marked with two tick marks and one arrow each.

Be sure to supply the reasoning for each step.

If a pair of opposite sides is parallel and congruent then the quadrilateral is a parallelogram.
Use the if part of the statement as the givens, and the then part of the statement as the prove portion in the proof.

This flowchart has 8 bubbles. Bubble # 1 has an arrow, pointing down to bubble # 4. Bubble numbers 2, 3, and 4 have arrows, pointing down to bubble # 5. Bubble #5 has an arrow, pointing down to bubble #6. Bubble # 6 has an arrow, pointing down to bubble # 7. Bubble 7 has an arrow, pointing down to bubble # 8.

   Bubble # 1    

     

 Bubble # 2

 Bubble # 3    

 Bubble # 4

 Bubble # 5

 Bubble # 6      

 Bubble # 7

 Bubble # 8