Given: Quadrilateral ABCD is a parallelogram.
Prove: AB ≅ CD
BC ≅ AD
Proof:
Statements Reasons
1. Quadrilateral ABCD is a parallelogram. Given
2. ?
3. Draw AC, a transversal that cuts two pairs of parallel segments.
AB ∥ CD
BC ∥ AD Drawing a line segment
4. ∠CAB ≅ ∠ACD
∠BCA ≅ ∠CAD Alternate Interior Angles Theorem
5. m∠CAB = m∠ACD
m∠BCA =m∠CAD Definition of Congruent
6. AC = AC Reflexive Property of Equality
7. ? ASA criterion for congruence
8. AB ≅ CD
BC ≅ AD Corrsponding sides of congrurent triangles are congruent
10
What are the missing statement and reason in step 2 of the proof?
A.
Statement: AB ≅ CD, BC ≅ AD
Reason: given
B.
Statement: ∠BAC ≅ ∠ACD
Reason: Alternate Interior Angles Theorem
C.
Statement: ΔABC ≅ ΔCDA
Reason: SSS criterion for congruence
D.
Statement: AB ∥ CD, BC ∥ AD
Reason: definition of a parallelogram
D.
Statement: AB ∥ CD, BC ∥ AD
Reason: definition of a parallelogram