Special Parallelograms

Which statements are true of all squares? Check all that apply.

The diagonals are perpendicular. The diagonals are congruent to each other. The diagonals bisect the vertex angles. The diagonals bisect each other.

Consider the diagram and proof below. Given: WXYZ is a parallelogram, ZX ~= WY Prove: WXYZ is a rectangle. What is the missing reason in Step 7?

d. consecutive <s in a ~~ are supplementary

A quilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus. Which measures are true for the quilt piece? Check all that apply.

a = 60° The perimeter of the rhombus is 16 inches. The length of the longer diagonal is approximately 7 inches.

A square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year. Each diagonal of the square window measures 9 inches. What is the approximate total length of iron edging needed to create the square frame and the two diagonals?

a. 43.5 inches

The figure shown is a rhombus. Which equation is true regarding the angles formed by the diagonals and sides of the rhombus?

a. x + y = z

The perimeter of square JKLM is 48 units. What is the value of x?

b. 9

Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus.

b. AMB ~ CMB ~ CMD ~ AMD

The figure is a parallelogram. One diagonal measures 28 units. Is the figure a rectangle? Explain.

b. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles

Rhombus LMNO is shown with its diagonals. The length of LN is 28 centimeters. What is the length of LP?

c. 14 cm

What is the approximate side length of the square?

c. 4.2 units

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

c. 41 units

Rectangle PQRS is shown with its diagonals, PR and QS. What type of triangle is STR?

c. isosceles triangle

ABCD is a square. What is the length of line segment D.C.?

d. 13 units

The figure is a square. Its diagonals meet to form four right angles. What is the approximate value of x?

d. 5.7 units