Proofs Involving Quadrilaterals

Use the diagram to answer the question.

• 1

• 2

• 3

• 4

Fill in the missing reason for the proof.

• Opposite angles are congruent.

• Alternate interior angles formed by parallel lines are congruent.

• Vertical angles are congruent.

• CPCTC

Fill in the missing reason for the proof.

• If alternate interior angles are congruent, then the lines are parallel.

• Definition of parallelogram

• Definition of parallel lines

• Opposite sides of a parallelogram are congruent.

Choose the correct missing reasons for the proof.

• 4) CPCTC; 6)All quads are parallelograms

• 4) Alternate Interior Angles are congruent; 6) Definition of paralelogram

• 4)CPCTC; 6)Definition of parallelogram

• 4) Alternate Interior Angles are congruent; 6) All quads are parallelograms

Fill in the missing reasons for the proof.

• 5) Alternate Interior angles are congruent; 6) ASA

• 5) Alternate Interior angles are congruent; 6) AAS

• 5) Vertical Angles are congruent; 6) ASA

• 5) Vertical Angles are congruent; 6) AAS

The missing reason is the same for steps 2 and 4. What is the missing reason?

• If alternate interior angles are congruent, then the lines are parallel.

• If vertical angles are congruent, then the lines are parallel.

• Definition of parallelogram

• Alternate interior angles formed by parallel lines are congruent.