Which statement describes a parallelogram that must be a square? a parallelogram with opposite sides that are congruent and diagonals that bisect the angles. a parallelogram with a right angle and diagonals that bisect the angles. a parallelogram with a right angle and opposites sides that are congruent. a parallelogram with all sides congruent.

Consider a parallelogram with a right angle and diagonals that bisect the angles.

In the figure, ABCD is a parallelogram with ∠ A = 90°.

Since the opposite angles of a parallelogram are equal,

∠ A = ∠ C = 90° and ∠ B = ∠ D

Also, since adjacent angles of a parallelogram are supplementary,

∠ A + ∠ B = 180°

But, since ∠ A = 90°, ∠ B = 90° and ∠ D = 90°

Therefore, ∠ A = ∠ B = ∠ C = ∠ D.

Now, it is given that the diagonals bisect the angles.

Therefore, ∠ OAB = ∠ OBA = ∠ OBC = ∠ OCB = 45°

Consider, triangles OBA and OBC.

∠ OBA = ∠ OBC = 45°

and OB = OB (common)

Therefore, Δ OBA ≅ Δ OBC (SAS Rule)

By corresponding parts of congruent triangles,

AB = BC

Note that in a parallelogram, the opposite angles are congruent.

Therefore, AB = BC = CD = DA.

Hence, in the parallelogram ABCD, we have,

AB = BC = CD = DA and ∠ A = ∠ B = ∠ C = ∠ D = 90°

Hence, ABCD is a square.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions