Answer:
2. Statement:AB=CD and BC=AD
[tex]AB \parallel CD\; and \;BC \parallel AD[/tex]
Reason: Given .
8. Statement:[tex]AB \cong CD[/tex] and [tex]BC \cong AD[/tex]
Step-by-step explanation:
Given
A quadrilateral ABCD is a parallelogram
[tex]AB \parallel CD[/tex] and [tex]BC \parallel AD[/tex]
AB=CD and BC= AD
1. Statement: Quadrilateral ABCD is a parallelogram
Reason: Given
2. AB=CD and BC= AD ,
[tex]AB \parallel CD[/tex] and [tex]BC \parallel AD[/tex]
Reason: Given
3. Draw AC is a transversal line that cuts two pairs of parallel lines AB and CD , BC and AD.
Reason: Drawing a line segment.
4.[tex]\angle CAB \cong \angle ACD[/tex]
[tex]\angle BCA\cong \angle CAD[/tex]
Reason: Alternate interior angles theorem
5.[tex]m\angle CAB= m \angle ACD[/tex]
[tex]m\angle BCA= m \angle CAD[/tex]
Reason: Congruent angles have equal measures.
6. AC= AC
Reason : Reflexive property of equality.
7. ASA criterion for congruence [tex]\triangle ABC \cong \triangle ADC[/tex]
Reason : Angle-side_ Angle property of congruence
8. [tex]AB \cong CD[/tex] and [tex]BC \cong AD[/tex]
Reason : Corresponding sides of congruent triangles are congruent.
