Geometry
posted by DANIELLE .
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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