Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. Since a rhombus has all of these characteristics it too is considered a parallelogram.

Therefore, the statement is true.

Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. 

A trapezoid has one set of opposite parallel sides however, they are not congruent. The opposite angles of a trapezoid are also not congruent therefore, the statement is false.

Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. 

Since the statement only says that  is an quadrilateral that has . This does not give enough information. A trapezoid has one pair of parallel sides but is not a parallelogram, therefore the statement, "A quadrilateral  has   therefore,  is a parallelogram." is false.

Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.

Since the angles given represent those in a parallelogram, and the opposite sides are congruent, that makes the figure a parallelogram.

Therefore, the statement is true.

Given the statement:

"Bisecting a parallelogram along one of its diagonal creates two congruent triangles."

Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. When a parallelogram is bisected along one of its diagonals it in fact creates two congruent triangles.

Therefore, the statement is true.

Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. 

Since the statement gives one pair of sides and one pair of angles but does not specify whether the pairs are opposite it cannot be determined whether the figure is a parallelogram or not.

Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other. 

Since an isosceles triangle has two side lengths that are equal, if it is reflected over the base a rhombus is created which is a type of parallelogram.

If the isosceles triangle is rotated so that one of the sides is the diagonal of the parallelogram then the opposite sides of the parallelogram are congruent thus making the figure a parallelogram.

If side lengths are added the resulting image will have three equal sides and one side that isn't therefore, the new figure is not a parallelogram.

Thus, looking at the given answer options, "Draw a reflected isosceles triangle where the base is shared and becomes the diagonal of the parallelogram." is the best choice.

Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.

Therefore, the statement is true.

Both squares and rhombi are quadrilaterals and parallelograms. Quadrilaterals are four sided figures and parallelograms are figures that have opposite sides that are parallel.

Squares by definition contain four  angles; rhombi on the other hand have two sets of opposite congruent angles. Therefore, for a square to to altered into a rhombus, the interior angles must be altered.

Rigid motion follows these criteria because the motion is rigid meaning that everything that is moving stays the same except for the location of the entire figure.  There are three common types of rigid motion; translation, reflection, and rotation.