Posted by **DANIELLE** on Wednesday, June 13, 2007 at 1:35pm.

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 congruent 6. Transitive prop 7 . AB=BC 7. Sides oposite are congruent angles

8.<1 & <2 8. Cor.parts are eual

9. AB=BC=CD=DA 9. ABCD is a rhombus

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