SOLUTION: Given: parallelogram ABCD side AD is congruent to side AB Prove: ABCD is a rhombus I need fast help

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Question 188432: Given: parallelogram ABCD
side AD is congruent to side AB
Prove: ABCD is a rhombus I need fast help
Answer by solver91311(24713) About Me  (Show Source):
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ABCD is a parallelogram. Given.

AD congruent to AB. Given.

AD = AB. Definition of congruence

AB congruent to DC and AD congruent to BC. Definition of a parallelogram.

AB = DC and AD = BC. Definition of congruence.

If AB = AD and AB = DC, then AB = DC. Reflexive property of equality

If AD = AB and AD = BC, then AB = BC. Reflexive property of equality

In summary, AB = AD = DC = BC. Hence, ABCD is a parallelogram with 4 equal sides.

Therefore, ABCD is a rhombus. Definition of a rhombus.

QED.

John