SOLUTION: Given: parallelogram ABCD
side AD is congruent to side AB
Prove: ABCD is a rhombus I need fast help
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS
Given: rhombus ABCD, E is the midpoint of DF
PROVE: AD is congruent to... (answered by Edwin McCravy)
given: ABCE is an isosceles trapezoid with ray AB is parallel to ray EC, and ray AE is... (answered by Theo)
i need help with this proof given:parallelogram abcd m is midpoint of line seg ab n is... (answered by ly12603)
Prove: if diagonal of a parallelogram bisects an angle of the parallelogram, then the... (answered by richard1234)
given: ABCD is a parallelogram
prove: < A congruent to < C, < B congruent to <... (answered by Edwin McCravy)
Hi! How Are You?! im having trouble with this proof can u please help me?!
Rhombus... (answered by Mathtut)
prove parallelogram ABCD is a rhombus(question)
given: AC bisects angles BAD and BCD... (answered by orca)
ABCD IS A RHOMBUS: if Ab=11, find... (answered by Edwin McCravy)
Given: ABCD is a parallelogram
Prove: angle DAB is congruent to... (answered by richwmiller)