Question

URGENT HELP PLEASE!

Proof:
Statement Reason
1. Quadrilateral ABCD is a parallelogram. given
2.
3. Draw . is a transversal that cuts
two pairs of parallel lines: and
and and . drawing a line segment
4. ∠CAB ≅ ∠ACD
∠BCA ≅ ∠CAD Alternate Interior Angles Theorem
5. m∠CAB = m∠ACD
m∠BCA = m∠CAD Congruent angles have equal measures.
6. AC = AC Reflexive Property of Equality
7. ASA criterion for congruence
8.
Corresponding sides of congruent triangles are congruent.

Answer 1

Statement: AB≈CD, BC≈AD
Reason: given

Answer 2

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`

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.