Question

URGENT HELP PLEASE!

Answer 1

Answer:

2. Statement:AB=CD and BC=AD

   $AB \parallel CD\; and \;BC \parallel AD$

Reason: Given .

8. Statement:$AB \cong CD$ and $BC \cong AD$

Step-by-step explanation:

Given  

A quadrilateral ABCD is a parallelogram

$AB \parallel CD$ and $BC \parallel AD$

AB=CD and BC= AD

1. Statement: Quadrilateral ABCD is a parallelogram

Reason: Given

2. AB=CD and BC= AD ,

$AB \parallel CD$  and $BC \parallel AD$

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.$\angle CAB \cong \angle ACD$

$\angle BCA\cong \angle CAD$

Reason: Alternate interior angles theorem

5.$m\angle CAB= m \angle ACD$

$m\angle BCA= m \angle CAD$

Reason: Congruent angles have equal measures.

6. AC= AC

Reason : Reflexive property of equality.

7. ASA criterion for congruence  $\triangle ABC \cong \triangle ADC$

Reason : Angle-side_ Angle property of congruence

8. $AB \cong CD$ and $BC \cong AD$

Reason : Corresponding sides of congruent triangles are congruent.

Answer 2

Statement: AB≈CD, BC≈AD
Reason: given