Question

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Answer 1

Answer:

      Statement ${}$                                                    Reason

1. Parallelogram ABCD  ${}$                                    1. Given

2. Side AD is parallel to side BC  ${}$                    2. Definition of a parallelogram

3. Side AB is a transversal of AD and BC  ${}$      3. Definition of a transversal

4. ∠A and ∠B are same side interior angles  ${}$ 4. Definition of SSIA

5. ∠A and ∠B are supplementary  ${}$                  5. SSIA between parallel lines

6. Side CD is a transversal of AD and BC  ${}$      6. Definition of a transversal

7. ∠C and ∠D are same side interior angles  ${}$ 7. Definition of SSIA

8. ∠C and ∠D are supplementary  ${}$                  8. Same Side Interior Angles,

                                              ${}$                                 SSIA, theorem

Step-by-step explanation:

Given that the quadrilateral ABCD is a parallelogram, we have;

Side AD is parallel to side BC, and side AB is a common transversal to AD and BC

∠A and ∠B are same side interior angles, SSIA, formed between parallel lines, therefore, according to Same Side Interior Angles theorem, we have;

∠A and ∠B are supplementary angles and therefore, ∠A + ∠B = 180°

Similarly, the angles ∠C and ∠D formed by the transversal CD and the parallel sides AD and BC are same side interior angles

∴ ∠C and ∠D are supplementary angles and ∠∠C + ∠D = 180°