SOLUTION: A parallelogram is a ___________ if and only if it has at least one right angle and four congruent sides. a. rectangle b. square c. rhombus d. none Please provide detail e

Question 472082: A parallelogram is a ____________ if and only if it has at least one right angle and four congruent sides.
a. rectangle
b. square
c. rhombus
d. none
Please provide detail explanation. Thanks.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If a parallelogram has one right angle, then the other angles are right angles (since the opposite angle is equal and the adjacent angles are supplementary).

So there are 4 right angles. Since we have 4 right angles and 4 congruent sides, we have a square.

So...

A parallelogram is a square if and only if it has at least one right angle and four congruent sides

making the answer choice B.
RELATED QUESTIONS
Question 1~ A quadrilateral with congurent diagonals. Choices A) A parallelogram B) A... (answered by rapaljer)

If a quadrilateral has at least one right angle, then it is a... (answered by Alan3354)

If parallelogram ABCD has congruent diagonals, the parallelogram must be a square... (answered by ewatrrr)

On a blueprint for a house, if the master bedroom is a parallelogram with at least one... (answered by jim_thompson5910)

Draw a valid conclusion from the following argument or write �no conclusion is possible.� (answered by robertb)

a parallelogram with opposite sides that are equal, or congruent, and with four right... (answered by Mathtut)

True or False--If a parallelogram has equal diagonals, then it is a rectangle Tue or... (answered by stanbon)

True or false and explain? If one pair of opposite sides of a quadrilateral is... (answered by tazoftroy)

The vertices of parallelogram IJKL are I(-2,1), J(2,4), K(2,-1), and L(-2,-4). Which... (answered by jojo14344)