I really need some help please!!!!!

Am I on the right tract?
Given: ABCD is a parallelogram; <1 is congruent to <2

To Prove: ABCD is a Rhombus

Plan: Show <2 is congruent to < CAB.
hence CB is congruent to AB,
making ABCD a parallelogram
with consecutive sides congruent

PROOF

Statements Reasons
1. ABCD is a parallelogram 1.Given
<1 is congruent to <2
2. Draw segment from A to C 2. Two points determine exactly one line
3.< 1 & <3 are congruent 3. Alternate angles are congruent
4. AC bisects angle 1&2 4. Def. of Angle bisector
5 . m<DAB=m<BCD 5. Opposite angles in a parallelogram are equal
6. <2 & <3 are congruen6.Transitiveprop 7 .AB=BC 7. Sides oposite are
congruent angles
8.<1&<2 8. Cor.parts are equal
9.AB=BC=CD=DA 9. ABCD is a rhombus

I cant follow it without a diagram, sorry.

I sorry but I don't know how to use the computer to draw.

No problem! I can still help you understand the proof without a diagram. Let's break down the steps.

Given:
1. ABCD is a parallelogram.
2. <1 is congruent to <2.

To Prove:
ABCD is a rhombus.

Plan:
1. Show <2 is congruent to <CAB.
2. This implies that CB is congruent to AB.
3. Conclude that ABCD is a parallelogram with consecutive sides congruent.

Proof:
Statements Reasons
1. ABCD is a parallelogram Given
2. <1 is congruent to <2 Given
3. Draw segment from A to C Two points determine exactly one line
4. <1 and <3 are congruent Alternate angles are congruent
5. AC bisects angle 1 and 2 Definition of Angle bisector
6. m<DAB = m<BCD Opposite angles in a parallelogram are equal
7. <2 and <3 are congruent Transitive property
8. AB = BC Sides opposite to congruent angles are congruent
9. <1 and <2 Corresponding parts of congruent angles are equal
10. AB = BC = CD = DA Consecutive sides of a parallelogram are congruent, making ABCD a rhombus

I hope this helps clarify the steps of the proof for you!

You don't need to know how to draw, copy and paste the image on the site. Or give the link of the image, and it can be viewed.