Which statement describes a parallelogram that must be a square? A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other. B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.C. A parallelogram with a right angle and diagonals that are congruent D. A parallelogram with diagonals that bisect each other.
Accepted Solution
A:
Answer: B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.Step-by-step explanation:We know that a parallelogram is a quadrilateral having congruent opposite sides and its diagonals bisect each other.A square is a kind of parallelogram having all its consecutive sides equal and both diagonals congruent to each other.Its all 4 angles are right angle.let's check all the statements :A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.
→It can be rhombus ∵ it also has same characteristics.B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
→ It only occurs in square.C. A parallelogram with a right angle and diagonals that are congruent
.→ it can be a rectangle ∵ it has all its angles right angle and diagonals are congruent.D. A parallelogram with diagonals that bisect each other.→ It is the basic property of parallelogram , it can describe a rhombus or rectangle both.